Locally active memristor (LAM), which has an ability to amplify fluctuations, is a natural component for constructing artificial neuron circuits. This paper proposes a novel third-order neuron circuit by paralleling two LAMs and a capacitor. Firstly, two parallel LAMs are equivalently modeled as a second-order LAM to facilitate theoretical analysis. Regarding the third-order neuron, the parameter design and operating condition are obtained by calculating its small signal impedance functions poles or Jacobin matrixs eigenvalues. It is demonstrated that the neuron exhibits various neuromorphic behaviors, including periodic spiking, chaos and burst-number adaptation. Due to the two different LAMs, the proposed thirdorder system has multiple equilibrium points, leading to the generation of coexisting attractors. Interestingly, the generated chaotic attractor does not revolve around a single unstable equilibrium point, but is located between two unstable equilibrium points. Furthermore, the emergence of oscillating behaviors is dependent on the distance between the two unstable equilibrium points. Detailed theoretical and simulation analysis are presented to investigate the neuron dynamics and provide an explanation for the observed neuromorphic behaviors. Finally, physical circuit implementation of the neuron is constructed based on the memristor emulator, which also demonstrates the practicability of the proposed neuron model and the correctness of the theoretical analysis.

Resource competition and intentional disruptions, grounded in rational intergroup conflict theory, play a central role in driving strategic rivalry in networked games. These mechanisms mirror real-world conflict dynamics, profoundly shaping decision-making processes and interfering with systemic stability. This study investigates the modeling and dynamics of networked evolutionary games with intergroup conflict (NEGs-IC). In the proposed framework, players are assigned a finite number of health points, which decrease when attacked–affecting both survivability and strategic interactions. Leveraging logical dynamical system modeling, we capture the co-evolution of strategies, payoffs, health points, and player actions, demonstrating that NEGs-IC can be effectively represented as a logical dynamic system. To characterize collective interest in NEGs-IC, we introduce an objective function that balances group cooperation and health point attrition. Based on this formulation, we define three evaluation criteria–optimal, suboptimal, and weak–to assess collective interest. An illustrative example is also presented to analyze network-based conflicts, offering insights into strategic behavior in adversarial environments.

This work is concerned with mean-square bipartite containment of second-order multileader multiagent systems (MASs), contaminating compound noise, and antagonistic information under a fixed or Markovian switching signed topology. A new class of bipartite containment control protocols based on absolute velocity and relative position information is designed using signed graphs, and a time-varying control gain is introduced to eliminate the combined effect of additive and multiplicative noises. For the case under fixed topology, sufficient conditions for achieving bipartite containment are derived by using the Lyapunov function method. Then, it is extended to the case of nonlinear dynamics. Specific convergence values for all leaders and followers are obtained. For the case under Markovian switching topology, the boundedness of the agents' states and noise intensity is proved by employing the extended second-moment method. By utilizing properties of stochastic matrices and the ergodicity of Markov chains, the second moments of the bipartite containment errors are estimated to obtain mean-square bipartite containment conditions. In addition, the corresponding convergence rates of mean-square errors are explicitly expressed. The effectiveness of the theoretical results is finally verified through numerical simulations.

Yang Sun, Guanrong Chen, Hamid Alinejad-Rokny, Jianzhu Bao, Yuqi Huang, Bin Liang, Kam-Fai Wong, Min Yang, Ruifeng Xu. Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2025.

This paper investigates the cooperative fuzzy tracking control of nonlinear unmanned surface vehicles with input quantization and event-triggered mechanism. The proposed cooperative control scheme consists of two parts: (i) the distributed observer and (ii) the dynamic event-based fuzzy tracking controller. The distributed observer is designed to obtain the nonlinear leader’s trajectory information on a directed communication topology. Under this framework, uncertain nonlinearity within the vehicle model is approximated through fuzzy logic systems, and, according to the state of the distributed observer, the dynamic event-based adaptive fuzzy tracking control law is developed with an input switching quantizer. Furthermore, a prescribed performance method is introduced to ensure the transient performance of tracking errors and obtain zero-tracking errors ultimately, which is proved through Lyapunov stability theory. Finally, the effectiveness of the proposed control strategy is verified by simulation experiments.

Understanding the communication and information processing mechanisms in pinning control is highly influenced by the connectivity structure of the network, particularly in higher-order networks. However, existing studies predominantly focus on static network structures and utilize complete error information, often neglecting underlying inter-node dependencies, thereby limiting the effectiveness of low-energy control in higher-order dynamic systems. To address these limitations, this paper proposes a novel pinning control scheme for the synchronization of inertial memristive neural networks (IMNNs) based on dynamic Granger causality analysis (DGCA). First, an interpretable IMNN model is constructed to explicitly characterize higher-order interactions without decomposing the system into first-order subsystems. Then, unlike traditional pinned-node selection strategies relying on static interaction rules, a causality-aware selection algorithm is developed using DGCA to dynamically identify influential nodes via time-series analysis, enhancing control efficiency under dynamic network conditions. Furthermore, a local information-based pinning controller is designed by leveraging local causal relationships and control influence regions extracted from DGCA, ensuring the stability of the synchronization error system. Theoretical guarantees are provided by deriving sufficient conditions for controller design based on Lyapunov stability theory. Finally, three numerical examples are presented to demonstrate the effectiveness and practicality of the proposed scheme.

The static architecture of artificial neural networks has fixed synaptic weights, whose connections do not change according to new information or learning experience. In contrast, the capacity of synaptic weight empowers biological neural networks to learn and adapt to diverse tasks, resulting in various dynamical behaviors. In this paper, a novel memristor model is designed into the Hopfield neural network for generating any desired number of multi-scroll attractors. Offset booster provides a channel for distance regulation and number control of coexisting attractors. Independent offset boosters determine the coexisting patterns including the types of one-scroll attractor, two-scroll attractor, four-scroll attractor, and other mixed types. In addition, the digital circuit platform of CH32V307 is applied to verify numerical simulations. Finally, the chaotic data generated in the memristive Hopfield neural network is introduced into the northern goshawk optimization (MHNN-NGO), by which the full network optimization is achieved.

Chua corsage memristor (CCM) is characterized by its local activity and can be used to construct neuron circuits. Edge of chaos is a subset of the locally active domain, which is responsible for the emergence of complexity and neuromorphic behaviors. When two identical resting “dead” CCM neurons poised on the edge of chaos are coupled through a linear passive resistor, these two neurons can be activated and a couple of oscillations appear. This phenomenon is referred to as the Smale paradox, which has not been observed from hardware circuits. The present paper addresses this issue by proposing the stability criterion of the two-port coupled system using the small-signal analysis method and then derives an emergence condition of the Smale paradox based on two coupled “dead” CCM neurons in terms of the parameter value ranges. Simulation results demonstrate the correctness of the theoretical analysis. Interestingly, anti-phase synchronization is observed after two identical neurons are coupled with a linear resistor, which is different from the traditional in-phase synchronization between resistively coupled oscillators. The resistively coupled memristive neurons are implemented by hardware based on the poor man’s circuit. The experimental results confirm the reproduction of the Smale paradox and reveal the effect of the coupling resistance on the dynamics of the system.

This paper addresses the problem of distributed online generalized Nash equilibrium (GNE) learning for multi-cluster games with delayed function feedback. Specifically, each agent in the game is assumed to be informed of a sequence of local cost functions and constraint functions, which are known to the agent with time-varying delays subsequent to decision-making at each round. The objective of each agent within a cluster is to collaboratively optimize the cluster’s cost function, subject to time-varying coupled inequality constraints and local constraint sets over time. Additionally, it is assumed that each agent is required to estimate the decisions of all other agents through interactions with its neighbors, rather than directly accessing the decisions of all agents, i.e., each agent needs to make decisions under partial-decision information. To solve such a challenging problem, a novel distributed online delay-tolerant GNE learning algorithm is developed based upon the primal-dual algorithm with an aggregation gradient mechanism. The system-wise regret and the constraint violation are formulated to measure the performance of the algorithm, demonstrating sublinear growth with respect to the time horizon$\boldsymbol {T}$under certain conditions. Finally, numerical results are presented to verify the effectiveness of the proposed algorithm.

Evidences have manifested that unidirectional ring neural networks lack the ability to generate desired chaos. This paper formulates a novel memristor regulation (MR) approach to constructing a no-equilibrium bi-memristor unidirectional ring neural network (BMURNN), in which two distinct memristors are incorporated into a unidirectional ring neural network derived from the Hopfield neural network, with enhanced chaotic complexity, whereas one serving as a memristive synapse and the other as an emitter of electromagnetic radiation. Numerical simulations reveal that any desired number of multi-scroll hidden chaotic attractors can be generated from the BMURNN via the non-ideal multi-piecewise nonlinear memristor, while the time-controlled multi-scroll attractor growth is output from the periodic function memristor, demonstrating that the memristors can enhance the chaos complexity of the original unidirectional ring neural network. Additionally, diverse coexisting hidden attractors, that is, hidden heterogeneous/homogeneous multistability evoked by the memory attributes of memristors, can be dynamically regulated by varying the initial conditions. Finally, a digital circuit is designed and implemented based on CH32 to validate the numerical simulations and theoretical analyses, and a new pseudorandom number generator is devised to explore the BMURNN for practical applications. Performance analyses demonstrate its superiority and high randomness, providing further proof for the effectiveness of the proposed MR method.

Previous works withM-ary differential chaos shift keying (MDCSK) schemes are designed for resisting the impulsive noise of power line communication (PLC). However, real PLC channel environments are complex, existing schemes primarily address impulsive noise but do not effectively reflect the advantages of the system in a real PLC environment. This paper first discusses the bit-error-rate (BER) performance of the MDCSK system in Katayama PLC environments, and designs a derivation scheme of time slots-dependent BER. Then, based on the characteristics of periodic changes in the Katayama PLC channel environment, an adaptive-MDCSK (AD-MDCSK) is proposed to obtain better BER performance in such environments, which eliminates the need for a device to pre-check the BER. In the proposed scheme, the two types of MDCSK schemes are switched with the time slots period changing, where two categories of detectors are also changed correspondingly at the receiver. The BER of the AD-MDCSK is derived and analyzed regarding its effectiveness over Katayama PLC channel. The simulation results verify the accuracy of the design and show the superior performance of the proposed scheme. The BER performances of the proposed system are compared to other existing schemes, demonstrating its better BER performance.

This article investigates the controllability of networked sampled-data systems with various time delays on both control and transmission channels. Necessary and sufficient controllability conditions are first derived for systems with a single delay and then extended to systems with multiple delays. It is found that delays in control signals have no effects on the overall controllability. For a networked system whose topology matrix has only zero eigenvalues, delays of neither control nor transmission signals will affect the overall controllability. It is proved that an uncontrollable mode 1 of such a networked sampled-data system cannot be altered by arbitrary delays. Finally, the networked sampled-data system with first-order holders is discussed, which is modeled as a variant of time-delayed system, and some easy-to-verify algebraic conditions on the controllability are given based on matrix rank checking.

This artcle investigates the fusion estimation problem for renewable energy microgrids subject to relay transmissions and cyber-attacks. A filter-and-forward (FaF) relay strategy is adopted to ensure the reliable transmission of power signals from distributed sensors to the remote estimator. This strategy jointly accounts for both sensor-relay and relay-estimator channels when determining signal transmission, and relays with embedded filtering capabilities are considered essential for extracting relay signals from corrupted measurements. In addition, four stochastic sequences governed by Bernoulli distributions are employed to characterize denial-of-service and false data injection attacks, which occur randomly throughout the communication process. The principal objective is to improve estimation accuracy by constructing an estimation scheme capable of operating under the presence of FaF relays and hybrid attacks. Specifically, the proposed scheme consists of two main components: first, the design of a recursive filtering algorithm at each FaF relay for generating the relay signal, and second, the development of a sequential fusion estimation algorithm to enable accurate state estimation. Sufficient conditions are derived to guarantee the mean-square boundedness of both the filtering error and the estimation error. The effectiveness of the proposed estimation methodology is demonstrated through simulation experiments conducted on renewable energy microgrids in a wireless multisensor system.

Periodical time-delay scenario is often encountered in industrial manufacturing processes. However, the presence of time delays and periodical coefficients brings challenges to controller design and system analysis, which thereby hinders the performance improvement of such systems. In this work, the dynamics of milling systems are transformed into a time-invariant finite-dimensional uncertain model described by Fourier series and Padé approximation. An adaptive active control law is accordingly designed to stabilize such complex dynamics. With the assistance of LaSalle–Yoshizawa theorem, conditions are derived to guarantee sufficiently large stability regions of the corresponding closed-loop system. A numerical case study is conducted on a standard two degrees of freedom milling perturbation system to substantiate the superiority of the proposed adaptive active control technique in terms of enlarged stable operational regions.

Understanding the underlying graph structure of a nonlinear map over a particular domain is essential in evaluating its potential for real applications. In this paper, we investigate the structure of the associated functional graph of Chebyshev permutation polynomials over a ring$\mathbb {Z}_{p^{k}}$, with p being a prime number greater than three, where every number in the ring is considered as a vertex and the existing mapping relation between two vertices is regarded as a directed edge. Based on some new properties of Chebyshev polynomials and their derivatives, we disclose how the basic structure of the functional graph evolves with respect to parameter k. First, we present a complete and explicit form of the length of a path starting from any given vertex. Then, we show that the functional graph’s strong patterns indicate that the number of cycles of any given length always remains constant as k increases. Moreover, we rigorously prove the rules on the elegant structure of the functional graph and verify them experimentally. Our results could be useful for studying the emergence mechanism of the complexity of a nonlinear map in digital computers and security analysis of its cryptographic applications.

A protograph low-density parity-check (P-LDPC) code-based lossy coding system is proposed for compressing the Gaussian mixture model source, as a particular case of shipping transportation systems. The compression performance is benchmarked against the rate-distortion bounds for this source. Some effective methods are developed to improve both the encoder and the decoder to reduce the compression distortion. Experimental results demonstrate that the proposed methods achieve good performance while maintaining low complexity.

This article is concerned with the rapid classification issue for dynamical patterns consisting of sampling sequences in a relatively large-scale dynamical dataset constructed by benchmark Rossler systems. Specifically, based on a recently developed deterministic learning mechanism, a rapid dynamical pattern classification method is developed, which contains a modeling stage and a classification stage. In the modeling stage, a deterministic learning scheme is employed to accurately learn/model the inherent dynamics of the training dynamical patterns and store the acquired knowledge in a set of constant radial basis function (RBF) networks. In the classification stage, based on the trained RBF networks, a set of dynamical estimators is developed for real-time dynamic comparison. The generating recognition errors are then used to effectively represent the dynamic differences in real-time. To this end, the associated class label of the minimum recognition error is assigned to the test pattern also in real-time. To demonstrate the effectiveness of the proposed method, a relatively large-scale dynamical pattern dataset containing various dynamical behaviors is constructed by utilizing a deterministic chaos prospector (DCP) technique. The simulation results show that the new method achieves competitive classification performances compared to the state-of-the-art time-series classification method for the dynamical system classification task. In addition to performance advantages, the new method can perform real-time time-series classification with the first 10% of data achieving over 95% of accuracy based on the full-length data. Besides, the superiority of our method is demonstrated from various datasets in the UCR time-series classification (TSC) archive.

In this article, the design issue for an iterative learning controller is investigated for the cooperative-antagonistic system under the scheduling effects of random access protocol (RAP). In order to reflect the heterogeneous characteristic of the underlying system, the dynamics of each node in the cooperative-antagonistic system are described by a two-time-scale system. For the purpose of avoiding data collisions in signal transmissions, the so-called RAP is introduced to schedule the data exchanges among nodes, where the transmission opportunities of nodes are modeled by a sequence of random variables with certain transition probabilities. Considering that the mutual relationships may be cooperative and also competitive among nodes in many real-world networks, a novel cooperative-antagonistic-based iterative learning controller is developed to handle the tracking problem of the system dynamics. Sufficient conditions are obtained for the design of the controller parameters. Furthermore, the derived results are extended to the case that the transition probabilities for the RAP are partially unknown. Finally, a numerical example is presented to illustrate the effectiveness of the proposed iterative learning control (ILC) scheme.

Superdiffusion refers to the faster diffusion process in a multiplex network compared to that in an individual network. In this work, we study how interlayer connectivity affects the diffusion performance of a multiplex network. Based on spectral graph theory, we explore the principles of superdiffusion in multiplex networks. We prove that in a duplex network with identical structures, superdiffusion cannot occur under one-to-one interlayer connections. In addition, we prove that the dissimilarity of the Fiedler vector significantly enhances the network superdiffusion performance, which can lead to superdiffusion when selecting nodes with differential eigenvector components in the Fiedler vector for interlayer connections. We also prove that the upper bound of network diffusion with interlayer crossing-connections is limited by the maximum difference of the eigenvector components in the Fiedler vector. Finally, we verify the effectiveness of the theoretical results by numerical analysis.

Pinning control provides an effective approach to controlling large-scale networks and conserving control resources. This article presents a solution to pinning synchronization in directed networks with a precise index that measures the pinning synchronization capability of directed networks, capturing full topological information about the networks. Building upon this index, the article utilizes matrix analysis tools, such as the non-negative matrix theory and strongly connected decomposition to analyze the impact of network structures and controller parameters on the network synchronizability. Specifically, the study investigates the influence of the in-degree of unpinned nodes, the difference between in-degrees and out-degrees of nodes, strong connectivity components, and the linear feedback control gains on the network synchronizability. Moreover, the article addresses the challenge of optimally selecting pinned nodes by using a graph partitioning algorithm and a greedy node selection algorithm, which can be applied to effectively select pinned nodes in a large-scale network. Extensive simulations on a range of real-world directed networks validate the efficiency of the proposed algorithms and demonstrate their superiority over seven baseline algorithms.

The spread of epidemics is a complex process influenced by multiple social relations, including families, schools, and companies. Group interactions represented by a simplicial complex have been shown to impact the dynamics of epidemic transmission significantly. However, the previously proposed higher order contagion models only consider the propagation process within the higher order structure but lack a description of the consistency of the node states in the structure. To address this problem, we provide solutions to create a solvable network model that shows network clusters and node state consistency tendencies, capable of capturing the coexistence of interacting groups. We analyze the bistable region and epidemic threshold of the higher order propagation dynamics and explore the effect of the state update of the nodes on the model in: 1) random regular simplicial networks; 2) triangular simplex-lattice networks; 3) star-simplicial networks; and 4) heterogeneous simplicial networks. Our theoretical analysis, complemented by Monte Carlo numerical simulations, demonstrates that the proposed model accurately captures phase transitions and the bistable region created by higher order interactions. In addition, we find that the incorporation of intersimplex interaction mechanisms greatly reduces the epidemic threshold of the system and produces a larger bistable region, in which the dynamics of the system are heavily affected by the density and location of the initially infected nodes. Our findings contribute to a better understanding of higher order interactions in complex networked systems.

Circuits and systems, such as multidimensional and nonlinear ones, large-scale integration circuits, and power networks, play a significant role in the whole spectrum of science and technology, from basic scientific theories to various real-world applications. With the increasing demand from applications, it is vital to develop circuits and systems with high accuracy, stability, flexibility, and security through efficient learning, design optimization, and integrated implementation. The rapid advancement of artificial intelligence (AI) has fostered a symbiotic relationship between circuits and systems and AI in both theory and applications. On the one hand, research in circuits and systems on efficient learning, design optimization, and integrated implementation aided by AI has recently gained a promising development, where energy-efficient circuits and systems have a very broad range of applications. On the other hand, the utilization of AI in real-world applications has become indispensable for the optimization and implementation of circuits and systems with high efficiency and low-power computation. Overall, through advanced learning, optimization, and implementation driven by AI, efficient circuits and systems running in real-time with low power can be realized for wider applications.

Measuring the influence of scientists and their activities on science and society is important and indeed essential for many studies. Despite the substantial efforts devoted to exploring the influence’s measures and patterns of an individual scientific enterprise, it remains unclear how to quantify the mutual impact of multiple scientific activities. This work quantifies the relationship between the scientists’ interactive activities and their influences with different patterns in the AMiner dataset. Specifically, inflation treatment and field normalization are introduced to process the big data of paper citations as the scientist’s influence, and then the evolution of the influence is investigated for scientific activities in the citation and cooperation patterns through the Hawkes process. The results show that elite scientists have higher individual and interaction influences than ordinary scientists in all patterns found in the study, with permutation tests verifying the significance of the new findings. Moreover, the study compares the patterns found in two largest disciplines, i.e.,STEMandHumanities, revealing the higher value of individual influence inSTEMthan inHumanities. Furthermore, it is found that the opposite trend ofSTEMandHumanitiesin the cooperation pattern suggests different cooperation habits of scientists in different disciplines. Overall, this investigation provides a feasible approach to addressing the scientific influence issue and deepening the quantitative understanding of the mutual influence of multiple scientific activities in science and society.

With the rapid development of artificial intelligence, a number of machine learning algorithms, such as graph neural networks (GNNs), have been proposed to facilitate network analysis or graph data mining. Although effective, recent studies show that these advanced methods may suffer from adversarial attacks, i.e., they may lose effectiveness when only a small fraction of links are unexpectedly changed. This article investigates three well-known adversarial attack methods, i.e., Nettack, Meta Attack, and GradArgmax. It is found that different attack methods have their specific attack preferences on changing the target network structures. Such attack patterns are further verified by experimental results on some real-world networks, revealing that, generally, the top-4 most important network attributes on detecting adversarial samples suffice to explain the preference of an attack method. Based on these findings, the network attributes are utilized to design machine learning models for adversarial sample detection and attack method recognition with outstanding performance.

This article addresses the cooperative time-varying formation fuzzy tracking control problem for a cluster of heterogeneous multiple marine surface vehicles subject to unknown nonlinearity and actuator failures. The proposed cooperative control scheme consists of two parts: 1) a distributed time-varying formation observer and 2) a decentralized adaptive fuzzy tracking controller. The distributed observer is designed to obtain a predefined time-varying formation pattern under a directed communication topology. Subsequently, based on the states of the distributed observer, a decentralized fuzzy tracking control law is developed using fuzzy-logic systems and the adaptive approach. Lyapunov functions are constructed to guarantee that the controlled marine vehicles attain the desired time-varying formation with asymptotical stability of tracking errors. Finally, simulation results are presented to validate the efficacy of the proposed control methodology.

Network games primarily explore the intricacies of individual interactions and adaptive strategies within a network. Building upon this framework, the present study delves into the modeling, analysis, and control of heterogeneously networked evolutionary games with intergroup conflict (HNEG-IC), where attacking players possess area-monitoring capabilities with limited attacking power. To begin with, a mathematical model is introduced to capture intragroup strategy dynamics and intergroup conflicts of HNEGs-IC via the algebraic state space representation (ASSR). A necessary and sufficient condition for achieving global cooperation of HNEGs-IC is established. Then, a criterion for verifying the κ -cooperation below a certain mortality is presented. Considering the HNEGs-IC with strategy feedback control, it is proven that the feedback control, subject to global cooperation, is robust to conflicts when the intersection of the strategy threshold set and the reachable set of the preset initial strategy profiles is empty. Finally, for verification and demonstration, the obtained results are applied to a simplified virtual game model of the NATO and the Warsaw Pact.

The convergence rate and applicability to directed graphs with interaction topologies are two important features for practical applications of distributed optimization algorithms. In this article, a new kind of fast distributed discrete-time algorithms is developed for solving convex optimization problems with closed convex set constraints over directed interaction networks. Under the gradient tracking framework, two distributed algorithms are, respectively, designed over balanced and unbalanced graphs, where momentum terms and two time-scales are involved. Furthermore, it is demonstrated that the designed distributed algorithms attain linear speedup convergence rates provided that the momentum coefficients and the step size are appropriately selected. Finally, numerical simulations verify the effectiveness and the global accelerated effect of the designed algorithms.

Despite various measures across different engineering and social systems, network robustness remains crucial for resisting random faults and malicious attacks. In this study, robustness refers to the ability of a network to maintain its functionality after a part of the network has failed. Existing methods assess network robustness using attack simulations, spectral measures, or deep neural networks (DNNs), which return a single metric as a result. Evaluating network robustness is technically challenging, while evaluating a single metric is practically insufficient. This article proposes a multitask analysis system based on the graph isomorphism network (GIN) model, abbreviated as GIN-MAS. First, a destruction-based robustness metric is formulated using the destruction threshold of the examined network. A multitask learning approach is taken to learn the network robustness metrics, including connectivity robustness, controllability robustness, destruction threshold, and the maximum number of connected components. Then, a five-layer GIN is constructed for evaluating the aforementioned four robustness metrics simultaneously. Finally, extensive experimental studies reveal that 1) GIN-MAS outperforms nine other methods, including three state-of-the-art convolutional neural network (CNN)-based robustness evaluators, with lower prediction errors for both known and unknown datasets from various directed and undirected, synthetic, and real-world networks; 2) the multitask learning scheme is not only capable of handling multiple tasks simultaneously but more importantly it enables the parameter and knowledge sharing across tasks, thus preventing overfitting and enhancing the performances; and 3) GIN-MAS performs multitasks significantly faster than other single-task evaluators. The excellent performance of GIN-MAS suggests that more powerful DNNs have great potentials for analyzing more complicated and comprehensive robustness evaluation tasks.

This article investigates an energy-efficient formation control problem for multiagent systems with sampled data and random packet losses. A Bernoulli stochastic variable is used to describe packet losses, which is defined relative to the transmission energy consumed by antennas. A distributed sampled-data formation control law is designed and some analytic sufficient conditions on the formation control are derived. It is revealed that the sampling period, control parameters, network topology, as well as the transmission energy used by sensors impose inherent limitations in achieving the formation. Also, a method for searching the minimum allowable transmission energy is presented. Finally, numerical simulations are shown for illustration and verification.

Memristors have been extensively studied in the field of nonlinear dynamics. However, the dynamic regulation mechanism of memristor-induced hyperchaotic oscillation has not been focused. In this article, a 5-D memristive hyperchaotic oscillator with amplitude control and uncountably many attractors reflecting the arbitrary relocation of the dynamics is constructed and analyzed. In this system, one parameter embedded in the memristor is responsible for partial amplitude control. An independent constant is applied for offset boosting with two system variables. Also, variable boosting can be achieved by varying the initial values, indicating that the system has homogenous multistability, which is shown to have uncountably many continuously distributed attractors. This memristive system provides the first example with uncountably many coexisting hyperchaotic attractors without any periodic function involved. Circuit implementation verifies the theoretical analysis and numerical simulations. A manganese electrolysis experiment was proposed to verify the unique advantage of offset-controllable hyperchaotic current in industrial electrolysis.

Deep learning technology has found a promising application in lightweight model design, for which pruning is an effective means of achieving a large reduction in both model parameters and float points operations (FLOPs). The existing neural network pruning methods mostly start from the consideration of the importance of model parameters and design parameter evaluation metrics to perform parameter pruning iteratively. These methods were not studied from the perspective of network model topology, so they might be effective but not efficient, and they require completely different pruning for different datasets. In this article, we study the graph structure of the neural network and propose a regular graph pruning (RGP) method to perform a one-shot neural network pruning. Specifically, we first generate a regular graph and set its node-degree values to meet the preset pruning ratio. Then, we reduce the average shortest path-length (ASPL) of the graph by swapping edges to obtain the optimal edge distribution. Finally, we map the obtained graph to a neural network structure to realize pruning. Our experiments demonstrate that the ASPL of the graph is negatively correlated with the classification accuracy of the neural network and that RGP has a strong precision retention capability with high parameter reduction (more than 90%) and FLOPs reduction (more than 90%) (the code for quick use and reproduction is available at https://github.com/Holidays1999/Neural-Network-Pruning-through-its-RegularGraph-Structure).

Network robustness refers to the ability of a network to continue its functioning against malicious attacks, which is critical for various natural and industrial networks. Network robustness can be quantitatively measured by a sequence of values that record the remaining functionality after a sequential node- or edge-removal attacks. Robustness evaluations are traditionally determined by attack simulations, which are computationally very time-consuming and sometimes practically infeasible. The convolutional neural network (CNN)-based prediction provides a cost-efficient approach to fast evaluating the network robustness. In this article, the prediction performances of the learning feature representation-based CNN (LFR-CNN) and PATCHY-SAN methods are compared through extensively empirical experiments. Specifically, three distributions of network size in the training data are investigated, including the uniform, Gaussian, and extra distributions. The relationship between the CNN input size and the dimension of the evaluated network is studied. Extensive experimental results reveal that compared to the training data of uniform distribution, the Gaussian and extra distributions can significantly improve both the prediction performance and the generalizability, for both LFR-CNN and PATCHY-SAN, and for various functionality robustness. The extension ability of LFR-CNN is significantly better than PATCHY-SAN, verified by extensive comparisons on predicting the robustness of unseen networks. In general, LFR-CNN outperforms PATCHY-SAN, and thus LFR-CNN is recommended over PATCHY-SAN. However, since both LFR-CNN and PATCHY-SAN have advantages for different scenarios, the optimal settings of the input size of CNN are recommended under different configurations.

Data-based discovery of the underlying dynamics of nonlinear systems is of great importance to the prediction and control of engineering systems. This article presents a duplex neurodynamic learning (DNL) approach to the identification of discrete-time nonlinear systems subjected to both external disturbances and measurement noise. A neurodynamic learning method is proposed based on two-timescale recurrent neural networks (RNNs) for system identification. Truncated singular value decomposition is adopted to purify the data contaminated by external disturbances and measurement noises. Two RNNs are employed to cooperatively search for a global optimal solution, and the particle swarm optimization rule is used to reinitialize the RNNs upon the local convergence of the RNNs. The effectiveness and superiority of the proposed DNL method are demonstrated via simulations on benchmark chaotic and NARMAX systems.

This article investigates resilient distributed parameter estimation (RDPE) against sensor attacks with variable sparsity. First, the fixed sparsity of attacks is relaxed to variable sparsity over a specific time scale, with a sparse-varying sensor attack model proposed. Then, to counteract such attacks, an improved resilient distributed parameter observer is constructed by following the concept of sliding windows. Without altering the redundancy condition of sensor measurements, a sufficient condition to resist the sparsity-varying attacks is presented. Furthermore, under the assumption of accessible global historical attack detection information, the performance of RDPE is improved. Finally, some numerical simulation examples are presented to demonstrate the effectiveness of the proposed design.

A new edge centrality measure, connectivity rank index (CRI), is proposed based on the effect of an edge on the network algebraic connectivity. Compared with the existing indices, the CRI can determine the importance of a present edge as well as an absent edge. For large-scale networks, the algorithm based on original CRI definition has high-time complexity. Therefore, an approximation algorithm is designed using the eigenvector elements corresponding to the second smallest Laplacian eigenvalue. This algorithm can identify the most influential edges and the least influential ones easily, which reduces the time complexity from the exhaustive searching scheme with$O(N^{5})$to$O(N^{3})$in a network of size$N$. Some examples are shown to verify the effectiveness of the algorithm and the theoretical results.

Abstract It is well known that in many real networks, such as brain networks and scientific collaboration networks, there exist higher order nonpairwise relations among nodes, i.e. interactions between more than two nodes at a time. This simplicial structure can be described by simplicial complexes and has an important effect on topological and dynamical properties of networks involving such group interactions. In this paper, we study analytically resistance distances in iteratively growing networks with higher order interactions characterized by the simplicial structure that is controlled by a parameter $q$. We derive exact formulas for interesting quantities about resistance distances, including Kirchhoff index, additive degree-Kirchhoff index, multiplicative degree-Kirchhoff index, as well as average resistance distance, which have found applications in various areas elsewhere. We show that the average resistance distance tends to a $q$-dependent constant, indicating the impact of simplicial organization on the structural robustness measured by average resistance distance.

Blockchain has gained significant adoption in energy trading, offering benefits for both economy and environment. Consensus, in particular, is a decisive factor for blockchain-based energy trading systems to operate efficiently and securely. However, the consensuses currently applied have been criticized for being too energy intensive or not sufficiently decentralized, which counteracts the positive effect of energy trading. Besides, consensus and energy trading are treated separately in many energy trading blockchain-based studies. In this article, we propose a green and efficient consortium blockchain-enabled transaction system for energy trading, meeting the requirement of low energy consumption under security. We then design a two-stage consensus mechanism called proof-of-energy that is coupled to trading through “energy” and naturally uses the monetary rewards to stimulate prosumer participation. Specifically, it retains a strong degree of decentralization, which selects a dynamic delegation with high historical energy generation and motivates delegates to compete for new blocks by solving a meaningful puzzle. Furthermore, a variable block reward is investigated as the incentive to regulate trading and consensus behavior within a reasonable range of energy consumption. Finally, we design a two-layer iterative algorithm to obtain the optimal consensus strategy and block rewards, taking the noncooperative game approach with the consideration of the strategy effect on the pricing model. Our simulation results show that the proposed blockchain-enabled system has a high energy efficiency ratio that improves the social welfare and reduces the consensus overhead.

Information and communication technology tremendously facilitates the operation efficiency and economy of modern power systems in recent years. However, risks such as bandwidth constraints and malicious attacks threaten the secure load frequency control (LFC) of power systems. To mitigate such risks, this paper proposes distributed observer-based event-triggered LFC schemes for multi-area power systems under cyber attacks. Considering the practical situation that only local system output information may be available, distributed observer-based LFC schemes are designed. Meanwhile, to reduce the communication burden, an event-triggered mechanism is adopted to design control laws, where both static and dynamic event-triggered approaches are taken and the dynamic one is proved to be more economical in terms of control cost. Verifiable sufficient conditions are established to guarantee the stability of the closed-loop system in the presence of cyber attacks and the controller gains are explicitly derived. Finally, validation studies on a three-area interconnected power system are carried out to demonstrate the proposed control schemes. Note to Practitioners—Load frequency is a crucial index for evaluating the quality of electric energy and thus LFC has brought considerable attention in the area of power systems control. Although many achievements have been made on the LFC of multi-area power systems, the risks such as bandwidth constraints and malicious attacks affect the normal operation of LFC due to the interconnection between different power systems. To deal with these risks, this paper focuses on designing event-triggered LFC to guarantee the stability of the frequency deviation while reducing the communication burden and mitigating cyber attacks. More importantly, the proposed event-triggered LFC is designed based on an observer and can be implemented in a distributed manner, which is relatively practical in real applications. The results presented in this paper aim to provide a helpful reference for stable and secure LFC design of multi-area power systems, such that the corresponding application research can be promoted.

Load frequency control (LFC) is crucial for the economic operation and safety of power systems. Therefore this paper addresses the LFC problem for uncertain multi-area power systems with actuator failures. Specifically, actuator failures, uncertainties and communication bandwidth constraints appearing in multi-area power systems are taken into account simultaneously, and novel reliable event-triggered LFC schemes are proposed to cope with these troubles. The proposed schemes can ensure the asymptotical stability of the closed-loop system when only matched uncertainty exists. For the case of coexisting matched and mismatched uncertainties, the state trajectories of the closed-loop system can be controlled within a bounded set, where the size of the bounded set is only related to the mismatched uncertainty. To illustrate the theoretical results, a numerical example of three-area interconnected power system is presented. Note to Practitioners—Load frequency directly affects the quality of electric energy and is one of the main observation states of power systems, hence LFC has been widely investigated in the literature. For multi-area power systems, the system model to be controlled may be subjected to multiple unfavorable factors in practical situations, such as limited bandwidths, model uncertainties and actuator failures. To cope with these unfavorable factors, this paper is devoted to developing a unified control framework to guarantee the stability of the frequency deviation based on the event-triggered mechanism. Considering both matched and unmatched system uncertainties may exist as well as the bound of system uncertainties can be unknown, event-triggered control schemes including static event-triggered LFC and adaptive event-triggered LFC are accordingly designed to deal with aforementioned situations such that the closed-loop system is asymptotically or boundedly stable. The research outcome of this paper provides simple but effective LFC approaches that can be used to maintain the reliable and stable operation of multi-area power systems.

Knowledge of the Laplacian eigenvalues of a network provides important insights into its structural features and dynamical behaviours. Node or link removal caused by possible outage events, such as mechanical and electrical failures or malicious attacks, significantly impacts the Laplacian spectra. This can also happen due to intentional node removal against which, increasing the algebraic connectivity is desired. In this article, an analytical metric is proposed to measure the effect of node removal on the Laplacian eigenvalues of the network. The metric is formulated based on the local multiplicity of each eigenvalue at each node, so that the effect of node removal on any particular eigenvalues can be approximated using only one single eigen-decomposition of the Laplacian matrix. The metric is applicable to undirected networks as well as strongly-connected directed ones. It also provides a reliable approximation for the “Laplacian energy” of a network. The performance of the metric is evaluated for several synthetic networks and also the American Western States power grid. Results show that this metric has a nearly perfect precision in correctly predicting the most central nodes, and significantly outperforms other comparable heuristic methods.

This paper addresses the robustness of a network to sustain its connectivity and controllability against malicious attacks. This kind of network robustness is typically measured by the time-consuming attack simulation, which returns a sequence of values that record the remaining connectivity and controllability after a sequence of node- or edge-removal attacks. For improvement, this paper develops an efficient framework for network robustness prediction, the spatial pyramid pooling convolutional neural network (SPP-CNN). The new framework installs a spatial pyramid pooling layer between the convolutional and fully-connected layers, overcoming the common mismatch issue in the CNN-based prediction approaches and extending its generalizability. Extensive experiments are carried out by comparing SPP-CNN with three state-of-the-art robustness predictors, namely one CNN-based and two graph neural networks-based frameworks. Synthetic and real-world networks, both directed and undirected, are investigated. Experimental results demonstrate that the proposed SPP-CNN achieves better prediction performances and better generalizability for both cases of known and unknown datasets, with significantly lower time-consumption, than its counterparts.

A lossy source coding system based on the protograph low-density parity-check (P-LDPC) code is proposed for Gaussian source compression. In the proposed system, the conventional belief propagation (BP) algorithm is modified to be a concatenated BP-inverse BP (BP-$i$BP) for encoding and decoding, where the$i$BP is constructed by a fully-connected layer of a neural network. Compared to the existing approximate message passing algorithm, the proposed BP-$i$BP realizes a float-to-bit compression with low complexity for arbitrary Gaussian sources. The BP-$i$BP is implemented based on the linking relation of the protograph; therefore, it is necessary to optimally design the protograph to obtain better rate-distortion function (RDF) performance. Regarding the coding optimal procedure, a mutual information iteration convergence (MIIC) algorithm is designed as the optimal criterion to determine the source P-LDPC code with minimum distortion. Inspired by the plane construction of quantum stabilizer code, a lattice topological splicing (LTS) algorithm is proposed for regularly building the protograph to reduce the code searching complexity. By using the MIIC and the LTS algorithms, the BP-$i$BP based on the designed P-LDPC code maintains good distortion performance close to the RDF limit.

This article studies coordinated tracking of underactuated and uncertain autonomous surface vehicles (ASVs) via model-reference reinforcement learning control. It considered how model-reference control can be incorporated with reinforcement learning to address the challenges caused by model uncertainties and input underactuation, and how existing results may be employed to realize adaptive communication amongst ASVs. It is demonstrated that the proposed algorithm has a better performance over baseline control and effectively improves the training efficiency over reinforcement learning.

Removing noisy links from an observed network is a task commonly required for preprocessing real-world network data. However, containing both noisy and clean links, the observed network cannot be treated as a trustworthy information source for supervised learning. Therefore, it is necessary but also technically challenging to detect noisy links in the context of data contamination. To address this issue, in the present article, a two-phased computational model is proposed, called link-information augmented twin autoencoders, which is able to deal with: 1) link information augmentation; 2) link-level contrastive denoising; 3) link information correction. Extensive experiments on six real-world networks verify that the proposed model outperforms other comparable methods in removing noisy links from the observed network so as to recover the real network from the corrupted one very accurately. Extended analyses also provide interpretable evidence to support the superiority of the proposed model for the task of network denoising.

Network robustness is critical for various societal and industrial networks against malicious attacks. In particular, connectivity robustness and controllability robustness reflect how well a networked system can maintain its connectedness and controllability against destructive attacks, which can be quantified by a sequence of values that record the remaining connectivity and controllability of the network after a sequence of node- or edge-removal attacks. Traditionally, robustness is determined by attack simulations, which are computationally very time-consuming or even practically infeasible for large-scale networks. In this article, an improved method for network robustness prediction is developed based on learning feature representation using the convolutional neural network (LFR-CNN). In this scheme, the higher-dimensional network data are compressed into lower-dimensional representations, which are then passed to a convolutional neural network to perform robustness prediction. Extensive experimental studies on both synthetic and real-world networks, both directed and undirected, demonstrate that: 1) the proposed LFR-CNN performs better than other two state-of-the-art prediction methods, with significantly smaller prediction errors; 2) LFR-CNN is insensitive to the variation of the input network size, which significantly extends its applicability; 3) although LFR-CNN needs more time to perform feature learning, it can achieve accurate prediction faster than attack simulations; and 4) LFR-CNN not only accurately predicts the network robustness, but also provides a good indicator for connectivity robustness, better than the classical spectral measures.

This article investigates uniformly predefined-time bounded consensus of leader-following multiagent systems (MASs) with unknown system nonlinearity and external disturbance via distributed adaptive fuzzy control. First, uniformly predefined-time-bounded stability is analyzed and a sufficient condition is derived for the system to achieve semiglobally (globally) uniformly predefined-time-bounded consensus. Therein, the settling time is independent of initial conditions and can be defined in advance. Then, for first-order MASs, distributed adaptive fuzzy controllers are designed by combining neighboring consensus errors to drive all following agents to globally track the leader's state within predefined time. For second-order MASs, by formulating filtered errors, the consensus errors between following agents and the leader are shown to be bounded if the filtered errors are bounded. Furthermore, with the distributed controllers designed based on filtered errors, second-order MASs achieve semiglobally uniformly predefined-time-bounded leader-following consensus. Finally, two numerical examples are simulated, including: 1) a first-order leader-following MAS and 2) a second-order Lagrangian system consisting of single-link manipulators, to demonstrate the performance of the proposed controllers.

Applying the chaos theory for secure digital communications is promising and it is well acknowledged that in such applications the underlying chaotic systems should be carefully chosen. However, the requirements imposed on the chaotic systems are usually heuristic, without theoretic guarantee for the resultant communication scheme. Among all the primitives for secure communications, it is well accepted that (pseudo) random numbers are most essential. Taking the well-studied 2-D coupled map lattice (2D CML) as an example, this article performs a theoretical study toward pseudorandom number generation with the 2D CML. In so doing, an analytical expression of the Lyapunov exponent (LE) spectrum of the 2D CML is first derived. Using the LEs, one can configure system parameters to ensure the 2D CML only exhibits complex dynamic behavior, and then collect pseudorandom numbers from the system orbits. Moreover, based on the observation that least significant bit distributes more evenly in the (pseudo) random distribution, an extraction algorithm$\mathbf {E}$is developed with the property that when applied to the orbits of the 2D CML, it can squeeze uniform bits. In implementation, if fixed-point arithmetic is used in binary format with a precision of$z$bits after the radix point,$\mathbf {E}$can ensure that the deviation of the squeezed bits is bounded by$2^{-z}$. Further simulation results demonstrate that the new method not only guides the 2D CML model to exhibit complex dynamic behavior but also generates uniformly distributed independent bits with good efficiency. In particular, the squeezed pseudorandom bits can pass both NIST 800-22 and TestU01 test suites in various settings. This study thereby provides a theoretical basis for effectively applying the 2D CML to secure communications.

Based on the closed operational laws in picture fuzzy numbers and strict triangular norms, we extend the Bonferroni mean (BM) operator under the picture fuzzy environment to propose the picture fuzzy interactional Bonferroni mean (PFIBM), picture fuzzy interactional weighted Bonferroni mean (PFIWBM), and picture fuzzy interactional normalized weighted Bonferroni mean (PFINWBM) operators. We prove the monotonicity, idempotency, boundedness, and commutativity for the PFIBM and PFINWBM operators. We also establish a novel multicriteria decision making (MCDM) method under the picture fuzzy environment by applying the PFINWBM operator. Furthermore, we apply our MCDM method to the enterprise resource planning (ERP) systems selection. The comparative results for our MCDM method induced by six classes of well-known triangular norms ensure that the best selection is always the same ERP system. Therefore, our MCDM method is effective for dealing with the picture fuzzy MCDM problems.

All intuitionistic fuzzy TOPSIS methods contain two key elements: (1) the order structure, which can affect the choices of positive and negative ideal-points, and construction of admissible distance/similarity measures; (2) the distance/similarity measure, which is closely related to the values of the relative closeness degrees and determines the accuracy and rationality of decision-making. For the order structure, many efforts are devoted to constructing some score functions, which can strictly distinguish different intuitionistic fuzzy values (IFVs) and preserve the natural partial order for IFVs. This paper proves that such a score function does not exist. For the distance or similarity measure, some examples are given to show that classical similarity measures based on the Euclidean distance and Minkowski distance do not meet the axiomatic definition of IF similarity measures. Moreover, some illustrative examples are given to show that classical intuitionistic fuzzy TOPSIS methods do not ensure the monotonicity with the natural partial order or linear orders, which may yield some counter-intuitive results. To overcome the limitation of non-monotonicity, we propose a novel intuitionistic fuzzy TOPSIS method, using three new admissible distances with the linear orders measured by a score degree/similarity function and accuracy degree, or two aggregation functions, and prove that the proposed TOPSIS method is monotonous under these three linear orders. This is the first result with a strict mathematical proof on the monotonicity with the linear orders for the intuitionistic fuzzy TOPSIS method. Finally, we show two practical examples to illustrate the efficiency of the developed TOPSIS.

The COVID-19 pandemic brought not only global devastation but also an unprecedented infodemic of false or misleading information that spread rapidly through online social networks. Network analysis plays a crucial role in the science of fact-checking by modeling and learning the risk of infodemics through statistical processes and computation on mega-sized graphs. This article proposes MEGA, Machine Learning-Enhanced Graph Analytics, a framework that combines feature engineering and graph neural networks to enhance the efficiency of learning performance involving massive graphs. Infodemic risk analysis is a unique application of the MEGA framework, which involves detecting spambots by counting triangle motifs and identifying influential spreaders by computing the distance centrality. The MEGA framework is evaluated using the COVID-19 pandemic Twitter dataset, demonstrating superior computational efficiency and classification accuracy.

Community detection, which focuses on clustering vertex interactions, plays a significant role in network analysis. However, it also faces numerous challenges like missing data and adversarial attack. How to further improve the performance and robustness of community detection for real-world networks has raised great concerns. In this paper, we explore robust community detection by enhancing network structure, with two generic algorithms presented: one is named robust community detection via genetic algorithm (RobustECDGA), in which the modularity and the number of clusters are combined in a fitness function to find the optimal structure enhancement scheme; the other is called robust community detection via similarity ensemble (RobustECD-SE), integrating multiple information of community structures captured by various vertex similarities, which scales well on large-scale networks. Comprehensive experiments on real-world networks demonstrate, by comparing with two traditional enhancement strategies, that the new methods help six representative community detection algorithms achieve more significant performance improvement. Moreover, experiments on the corresponding adversarial networks indicate that the new methods could also optimize the network structure to a certain extent, achieving stronger robustness against adversarial attack. The source code of this paper is released on https://github.com/jjzhou012/robustECD release.

Memristor is an ideal electronic device used as an artificial nerve synapse due to its unique memory function. This article presents a design of a new Hopfield neural network (HNN) that can generate multiscroll attractors by utilizing a new memristor as a synapse in the HNN. Differing from the others, this memristor is constructed with hyperbolic tangent functions. Taking the memristor as a self-feedback synapse of a neuron in the HNN, the memristive HNN can yield multidouble-scroll attractors, and its parameters can be used to effectively control the number of double scrolls contained in an attractor. Interestingly, the generation of multidouble-scroll attractors is independent of the memductance function but depends only on the internal state equation. Thus, the memductance function can be adjusted to yield various complex dynamical behaviors. Moreover, amplitude control effects and quantitatively controllable multistability are revealed by numerical analysis. The accurate reproduction of some dynamical behaviors by a designed circuit verifies the correctness of the numerical analysis. Finally, based on the proposed memristive HNN, a novel image encryption scheme in the 3-D setting is designed and evaluated, demonstrating its good encryption performances.

One key factor affecting the distributed Nash equilibrium (NE) seeking in aggregative games is the unbalanced communication structure for multiple players. Although some results on seeking NE over undirected or weight-balanced graphs were established, how to address the distributed NE seeking problem over general directed communication graphs is still an outstanding challenge. This paper addresses the NE seeking problem for a class of aggregative games with general directed communication graphs. To achieve this objective, two new kinds of distributed discrete-time NE seeking algorithms are developed for aggregative games over fixed digraphs and time-varying digraphs, respectively. In particular, motivated by the heavy-ball method in optimization studies, a momentum term is introduced to the update law of the players’ actions and it is numerically verified that this momentum term accelerates the convergence of the proposed algorithms. For both strongly connected fixed graph and$B$-strongly connected time-varying graph, it is theoretically proved that the actions of players will converge to the NE of aggregative games for the case of decreasing step-size implemented by the proposed NE seeking algorithms if the cost functions and the aggregation of players satisfy some certain conditions. Finally, the developed NE seeking algorithms are applied to the energy consumption control of plug-in hybrid electric vehicles (PHEVs), which demonstrates the effectiveness of the theoretical results.

The trace of the controllability Gramian quantifies the average controllability in all directions in the system state space. In this paper, we investigate the average controllability of a semistable networked system with Laplacian dynamics and derive upper and lower bounds on the trace of its pseudo-controllability Gramian matrix. We show that these bounds are solely determined by the network topology, which can be obtained without computing any higher-dimensional matrix. We find that a sparse or a scale-free network is easy to control in terms of the average controllability. We then investigate the effect of the edges with negative weights on the average controllability for a signed network with Laplacian dynamics. We find that a small number of negatively-weighted edges can significantly affect the average controllability of the signed network. We finally demonstrate that many real-world networks are easy to control via manipulating negatively-weighted edges.

In conventional star-topology LoRa networks, the gateways are expected to collect the data from all the nodes nearby. However, a major challenge for the conventional LoRa system is the performance degradation due to the long-range communication over fading channels. To resolve the challenging issue, this paper investigates a two-hop amplify-and-forward relaying LoRa network in a two-dimension plane, where random nodal distances are considered. Moreover, a relay-selection mechanism is developed for the proposed system. Based on the best relay-selection protocol, the analytical bit-error-rate (BER) and asymptotic BER expressions, achievable diversity order, coverage probability, and throughput of the proposed system are derived over the Nakagami-$m$fading channel. Furthermore, to maximize the throughput of the proposed system, a two-dimensional resource allocation optimization problem (i.e., the spread factor selection and power allocation optimization) is formulated and investigated. The proposed optimal spread factor selection and power allocation scheme is verified to outperform the two baseline schemes. Simulation and numerical results show that although the proposed system reduces the throughput compared to the conventional LoRa system, it significantly improves the BER and coverage probability. Hence, the proposed system can be considered as a promising technique for low-power, long-range and highly reliable Internet-of-Things applications.

Switch-based adaptive dynamic programming (ADP) is an optimal control problem in which a cost must be minimized by switching among a family of dynamical modes. When the system dimension increases, the solution to switch-based ADP is made prohibitive by the exponentially increasing structure of the value function approximator and by the exponentially increasing modes. This technical correspondence proposes a distributed computational method for solving switch-based ADP. The method relies on partitioning the system into agents, each one dealing with a lower dimensional state and a few local modes. Each agent aims to minimize a local version of the global cost while avoiding that its local switching strategy has conflicts with the switching strategies of the neighboring agents. A heuristic algorithm based on the consensus dynamics and Nash equilibrium is proposed to avoid such conflicts. The effectiveness of the proposed method is verified via traffic and building test cases.

Link weight prediction is an important subject in network science and machine learning. Its applications to social network analysis, network modeling, and bioinformatics are ubiquitous. Although this subject has attracted considerable attention recently, the performance and interpretability of existing prediction models have not been well balanced. This article focuses on an unsupervised mixed strategy for link weight prediction. Here, the target attribute is the link weight, which represents the correlation or strength of the interaction between a pair of nodes. The input of the model is the weighted adjacency matrix without any preprocessing, as widely adopted in the existing models. Extensive observations on a large number of networks show that the new scheme is competitive to the state-of-the-art algorithms concerning both root-mean-square error and Pearson correlation coefficient metrics. Analytic and simulation results suggest that combining the weight consistency of the network and the link weight-associated latent factors of the nodes is a very effective way to solve the link weight prediction problem.

This article studies the distributed average tracking (DAT) problem pertaining to a discrete-time linear time-invariant multiagent network, which is subject to, concurrently, input delays, random packet drops, and reference noise. The problem amounts to an integrated design of delay and a packet-drop-tolerant algorithm and determining the ultimate upper bound of the tracking error between agents' states and the average of the reference signals. The investigation is driven by the goal of devising a practically more attainable average tracking algorithm, thereby extending the existing work in the literature, which largely ignored the aforementioned uncertainties. For this purpose, a blend of techniques from Kalman filtering, multistage consensus filtering, and predictive control is employed, which gives rise to a simple yet comepelling DAT algorithm that is robust to the initialization error and allows the tradeoff between communication/computation cost and stationary-state tracking error. Due to the inherent coupling among different control components, convergence analysis is significantly challenging. Nevertheless, it is revealed that the allowable values of the algorithm parameters rely upon the maximal degree of an expected network, while the convergence speed depends upon the second smallest eigenvalue of the same network's topology. The effectiveness of the theoretical results is verified by a numerical example.

This article analyzes the problem of the sliding-mode control (SMC) design for discrete-time piecewise nonhomogeneous Markov jump nonlinear systems (MJNSs) subject to an external disturbance with time-varying transition probabilities (TPs). A discrete-time asynchronous integral sliding surface is constructed, which yields matched-nonlinearity-free sliding-mode dynamics (SMDs). Then, by using the mode-dependent Lyapunov function technique, a sufficient condition is established for ensuring the stochastic stability of SMD with extended dissipation. The solution to designing controller gains is obtained. Moreover, an SMC law and an adaptive law are, respectively, derived for driving the system trajectories to move into a predetermined sliding-mode region with specified precision. Finally, the feasibility and effectiveness of the new design are verified and demonstrated by a simulation example.

This article surveys the interdisciplinary research of neuroscience, network science, and dynamic systems, with emphasis on the emergence of brain-inspired intelligence. To replicate brain intelligence, a practical way is to reconstruct cortical networks with dynamic activities that nourish the brain functions, instead of using only artificial computing networks. The survey provides a complex network and spatiotemporal dynamics (abbr. network dynamics) perspective for understanding the brain and cortical networks and, furthermore, develops integrated approaches of neuroscience and network dynamics toward building brain-inspired intelligence with learning and resilience functions. Presented are fundamental concepts and principles of complex networks, neuroscience, and hybrid dynamic systems, as well as relevant studies about the brain and intelligence. Other promising research directions, such as brain science, data science, quantum information science, and machine behavior are also briefly discussed toward future applications.

This article develops an identification algorithm for nonlinear systems. Specifically, the nonlinear system identification problem is formulated as a sparse recovery problem of a homogeneous variant searching for the sparsest vector in the null subspace. An augmented Lagrangian function is utilized to relax the nonconvex optimization. Thereafter, an algorithm based on the alternating direction method and a regularization technique is proposed to solve the sparse recovery problem. The convergence of the proposed algorithm can be guaranteed through theoretical analysis. Moreover, by the proposed sparse identification method, redundant terms in nonlinear functional forms are removed and the computational efficiency is thus substantially enhanced. Numerical simulations are presented to verify the effectiveness and superiority of the present algorithm.

In this article, the constrained optimization problem with its global objective function being the sum of convex local cost functions and the constraint being a closed convex set is researched. The aim of this study is to solve the researched problem in a distributed manner, that is, using only local computations and local information exchanges. Toward this end, two gradient-tracking-based distributed optimization algorithms are designed for the considered problem over weight-balanced and weight-unbalanced graphs, respectively. Since the classical projection method is unsuitable to handle the closed convex set constraint under the gradient-tracking framework, a new indirect projection method is employed in this article to deal with the involved closed convex set constraint. Furthermore, two time scales are introduced to complete the convergence analyses. In addition, under the condition that all local cost functions are strongly convex and L -smooth, it is proved that the algorithms with well-selected fixed step sizes have linear convergence rates.

Network controllability measures how well a networked system can be controlled to a target state, and its robustness reflects how well the system can maintain the controllability against malicious attacks by means of node removals or edge removals. The measure of network controllability is quantified by the number of external control inputs needed to recover or to retain the controllability after the occurrence of an unexpected attack. The measure of the network controllability robustness, on the other hand, is quantified by a sequence of values that record the remaining controllability of the network after a sequence of attacks. Traditionally, the controllability robustness is determined by attack simulations, which is computationally time consuming. In this article, a method to predict the controllability robustness based on machine learning using a convolutional neural network (CNN) is proposed, motivated by the observations that: 1) there is no clear correlation between the topological features and the controllability robustness of a general network; 2) the adjacency matrix of a network can be regarded as a grayscale image; and 3) the CNN technique has proved successful in image processing without human intervention. Under the new framework, a fairly large number of training data generated by simulations are used to train a CNN for predicting the controllability robustness according to the input network-adjacency matrices, without performing conventional attack simulations. Extensive experimental studies were carried out, which demonstrate that the proposed framework for predicting controllability robustness of different network configurations is accurate and reliable with very low overheads.

This work investigates the fixed-time distributed coordination control for multiple Euler-Lagrange systems and, in particular, addresses containment control with stationary/dynamic leaders as well as leaderless synchronization control. For the containment control scenario with stationary leaders, the subgraph associated with followers is directed. When dynamic leaders are involved, the information transfer between neighboring followers is bidirectional, for which a novel distributed estimator is developed. For the leaderless synchronization control scenario, the communication network among agents is unidirectional. Three fixed-time distributed control schemes are designed for the aforementioned three cases by applying the fixed-time stability theory. The convergence of the coordination control objectives can be achieved in a fixed time that does not depend on any initial conditions of agents' states, and the settling times are also explicitly derived. Finally, numerical simulations are presented to demonstrate the feasibility of the developed control strategies.

A striking discovery in the field of network science is that the majority of real networked systems have some universal structural properties. In general, they are simultaneously sparse, scale-free, small-world, and loopy. In this article, we investigate the second-order consensus of dynamic networks with such universal structures subject to white noise at vertices. We focus on the network coherenceHSOcharacterized in terms of the$\mathcal {H}_{2}$-norm of the vertex systems, which measures the mean deviation of vertex states from their average value. We first study numerically the coherence of some representative real-world networks. We find that their coherenceHSOscales sublinearly with the vertex number$N$. We then study analyticallyHSOfor a class of iteratively growing networks—pseudofractal scale-free webs (PSFWs), and obtain an exact solution toHSO, which also increases sublinearly in$N$, with an exponent much smaller than 1. To explain the reasons for this sublinear behavior, we finally studyHSOfor Sierpinśki gaskets, for whichHSOgrows superlinearly in$N$, with a power exponent much larger than 1. Sierpinśki gaskets have the same number of vertices and edges as the PSFWs but do not display the scale-free and small-world properties. We thus conclude that the scale-free, small-world, and loopy topologies are jointly responsible for the observed sublinear scaling ofHSO.

Network controllability robustness (CR) reflects how well a networked system can maintain its controllability against destructive attacks. Its measure is quantified by a sequence of values that record the remaining controllability of the network after a sequence of node-removal or edge-removal attacks. Traditionally, the CR is determined by attack simulations, which is computationally time-consuming or even infeasible. In this article, an improved method for predicting the network CR is developed based on machine learning using a group of convolutional neural networks (CNNs). In this scheme, a number of training data generated by simulations are used to train the group of CNNs for classification and prediction, respectively. Extensive experimental studies are carried out, which demonstrate that 1) the proposed method predicts more precisely than the classical single-CNN predictor; 2) the proposed CNN-based predictor provides a better predictive measure than the traditional spectral measures and network heterogeneity.

This article is concerned with the cluster consensus control problem for multiagent linear systems with a directed communication topology, where only relative output measurements of neighboring agents are available to each agent. Motivated by the pinning control technique, both static and dynamic intermittent output control strategies are proposed. Using Lyapunov functions, sufficient conditions are developed to ensure cluster consensus with existence-guaranteed control parameters. Both periodic and nonperiodic operations of intermittent controllers are investigated. Finally, the effectiveness of the theoretical results is demonstrated by a simulation example.

Formation control finds broad applications in numerous fields, such as cooperative detection, surveillance, transportation, and disaster rescue. In this article, aiming at hunting a moving target, a two-stage surrounding control algorithm is proposed for linear multiagent systems subject to input saturations. An adaptive distributed observer is developed for each agent to reconstruct the target’s position. With the assistance of the algebraic graph theory and low gain feedback technique, distributed controllers are designed to drive the agents to encircle the moving target with a fixed radius and evenly distributed phase angles. Finally, both numerical simulations and experiments are conducted to verify the effectiveness of the proposed control algorithm.

This article presents a novel technique for terminal-time synchronization of multivehicle systems. Taking sampled-data communications into account, the terminal-time synchronization problem of multivehicle systems is formulated as three demands. An estimation of terminal time is introduced for each vehicle, and a cooperative algorithm is designed based on motion planning to synchronize all estimated terminal times by using only local sampled-data information. The proposed algorithm not only can ensure the consensus of estimated terminal times at appointed time, but also can make the estimates finally be equal to the actual terminal times. To avoid Zeno behavior, the explicit expression of the norm of the consensus error is formulated, based on which the sampling interval sequence is modified to realize appointed-time approximate consensus of the actual terminal times. Local controller is also designed for each vehicle to ensure the fixed-time convergence of the relative velocity normal to the line of sight, and thus the singularity of control input at terminal time instant is successfully avoided. Experiments are performed to verify the effectiveness of the algorithms.

A CM2-S3 transmission link in wireless body area networks (WBAN) is implemented with a joint source channel coding (JSCC) system based on double protograph low-density parity-check (DP-LDPC) code pairs with high reliability and low power consumption. For the practicality and suitability considerations, the$M$-ary differential chaos shift keying scheme is introduced to modulate the CM2-S3 channel with better performance than the standard modulations in WBAN. Due to the non-Gaussian-like distribution of the CM2-S3 channel model, the initial joint protograph extrinsic information transfer (JPEXIT) algorithm does not work as a coding analysis tool. To solve this problem, a numerical Gaussian approximation is employed to modify the iterative mutual information function of the JPEXIT for achieving more precise output. Then, a joint code rate compatible (JCRC) method, designed with compatibility in resisting variable channel variances and adapting different source statistics, is proposed for optimizing the DP-LDPC code pairs. Based on the JCRC method, the code searching algorithm is simplified with lower complexity because of the reduced cycle-index. The simulation results show that optimized code pairs have better bit-error ratio performances compared to existing codes, which provides a strong technical support to promote high-quality data transmission in eHealthcare on the physical layer.

The joint source channel coding (JSCC) system is sensitive to the changing channel characteristics, because the optimally designed source-channel code pair always needs to be redesigned when the transmission environment is updated. A solution is to seek a common code pair for variable channels. Channel model 3 (CM3) is a variable on-body channel following the Weibull distribution, which is analyzed in four conditions due to varying shape factors, namely with exponential, Rayleigh, log-normal and normal distributions. The JSCC system is considered in this paper based on double protograph low-density parity-check (DP-LDPC) code pair over the variable CM3 channel. Firstly, four DP-LDPC code pairs are searched by the conventional differential evolution (DE) algorithm with four distributions of the Weibull model, respectively. However, these four code pairs only present good bit-error ratio performance in their own distribution, and have error floors in the other three. To resolve the problem, an artificial intelligence method based on principle component analysis (PCA) algorithm is designed to extract the common code pair. It is demonstrated that the common code pair performs well in noise-varying and practical-parameter transmissions. Instead of four DE code pairs, the designed one PCA code pair provides a strong technical support to low-complexity manufacturing such as eHealthcare.

The spectral radius of the non-backtracking matrix for an undirected graph plays an important role in various dynamic processes running on the graph. For example, its reciprocal provides an excellent approximation of epidemic and edge percolation thresholds. In this paper, we study the problem of minimizing the spectral radius of the non-backtracking matrix of a graph with n nodes and m edges, by deleting k selected edges. We show that the objective function of this combinatorial optimization problem is not submodular, although it is monotone. Since any straightforward approach to solving the optimization problem is computationally infeasible, we present an effective, scalable approximation algorithm with complexity O (n+km). Extensive experiment results for a large set of real-world networks verify the effectiveness and efficiency of our algorithm, and demonstrate that our algorithm outperforms several baseline schemes.

Memristors are widely used to construct multi-scroll/wing chaotic systems with complex dynamics. However, the generation of a multi-scroll/wing attractor is typically not induced by the memristor but depends on other nonlinear functions in the system, which does not take advantage of the unique features of the memristor for chaos-based applications. To address this issue, the present paper introduces a memristor coupling (MC) method to construct a novel memristive Sprott A system (MSAS) through coupling a flux-controlled memristor with multi-piecewise linear memductance into the chaotic Sprott A system. From theoretical analysis and numerical simulations, the MSAS is shown to be able to generate any number of multi-type hidden attractors, including multi-one-scroll, multi-double-scroll and multi-double-wing hidden attractors. In addition, it has two kinds of multistabilities, that is, heterogeneous multistability and homogeneous multistability. Based on these unique properties, different numbers of coexisting heterogeneous hidden attractors and coexisting homogeneous hidden attractors are derived respectively by switching the memristor initial states. These interesting dynamical properties are comprehensively investigated using nonlinear analysis tools. Furthermore, hardware experiments are implemented to demonstrate the feasibility of the MSAS and the effectiveness of the MC method. Finally, a new pseudo-random number generator (PRNG) is proposed to explore the practical applications of the MSAS. Performance evaluation results verify the high-quality randomness of the designed PRNG.

In this paper, the state estimation problem is investigated for a class of discrete nonlinear systems via sensor networks. A novel robust distributed extended Kalman filter, which can handle norm-bounded uncertainties in both the system model and its Taylor series expansion, is developed with ensured estimation performance. The filter is distributed in the sense that for each sensor, only its own measurements and its neighbors' information are utilized to optimize the upper bound of the estimation error covariance. Besides, a sufficient condition for the proposed algorithm is derived, which is simple and user-friendly since it depends on the property of the original nonlinear system instead of the estimation error covariance calculated at every step. Finally, the simulation results are presented to demonstrate the effectiveness of the filtering algorithm.

The optimal consensus problem of asynchronous sampling single-integrator and double-integrator multiagent systems is solved by distributed model predictive control (MPC) algorithms proposed in this article. In each predictive horizon, the finite-time linear-quadratic performance is minimized distributively by the control input with consensus state optimization. The MPC technique is then utilized to extend the optimal control sequence to the case of an infinite horizon. Conditions depending only on each agent's weighting scalar and sampling step are derived to guarantee the stability of the closed-loop system. Numerical examples of rendezvous control of multirobot systems illustrate the efficiency of the proposed algorithm.

We propose a novel epidemic model based on two-layered multiplex networks to explore the influence of positive and negative preventive information on epidemic propagation. In the model, one layer represents a social network with positive and negative preventive information spreading competitively, while the other one denotes the physical contact network with epidemic propagation. The individuals who are aware of positive prevention will take more effective measures to avoid being infected than those who are aware of negative prevention. Taking the microscopic Markov chain (MMC) approach, we analytically derive the expression of the epidemic threshold for the proposed epidemic model, which indicates that the diffusion of positive and negative prevention information, as well as the topology of the physical contact network have a significant impact on the epidemic threshold. By comparing the results obtained with MMC and those with the Monte Carlo (MC) simulations, it is found that they are in good agreement, but MMC can well describe the dynamics of the proposed model. Meanwhile, through extensive simulations, we demonstrate the impact of positive and negative preventive information on the epidemic threshold, as well as the prevalence of infectious diseases. We also find that the epidemic prevalence and the epidemic outbreaks can be suppressed by the diffusion of positive preventive information and be promoted by the diffusion of negative preventive information.

This article designs an effective consensus control protocol for continuous-time second-order time-delayed multiagent systems in a multiplicative noisy environment, using absolute velocity and relative position measurements. The nonlinear case and double-integrator case are studied, respectively. Due to the time delay and multiplicative noise in such models, the conventional methods for consensus analysis are not applicable. In this article, therefore, a degenerated Lyapunov functional is used to derive the conditions for mean-square consensus and almost-sure consensus, related to the Lipschitz constants of the nonlinear term, time delay, and noise intensity. In particular, for the double-integrator setting, it is shown that the mean-square consensus and the almost-sure consensus can be achieved by choosing appropriate control gains for any given time delay and noise intensity. To show the effectiveness of the proposed control protocol, some numerical simulations are demonstrated.

Topology identification of complex dynamical networks received extensive attention in the past decade. Most existing studies rely heavily on the linear independence condition (LIC). We find that a critical step in using this condition is not rigorous. Besides, it is difficult to verify this condition. Without regulating the original network, possible identification failure caused by network synchronization cannot be avoided. In this paper, we propose a new method to overcome these shortcomings. We add a regulation mechanism to the original network and construct an auxiliary network consisting of isolated nodes. Along with the outer synchronization between the regulated network and the auxiliary network, we show that the original network can be identified. Our method can avoid identification failure caused by network synchronization. Moreover, we show that there is no need to check the LIC. We finally provide some examples to demonstrate that our method is reliable and has good performances.

Gas-liquid two-phase flow is of great importance in various industrial processes. How to accurately measure the flow parameters in the gas-liquid two-phase flow remains a challenging problem. In this article, we develop a novel deep learning based soft measure technique to predict the gas void fraction, which is one key parameter in a gas-liquid two-phase flow. We conduct the vertical upward gas-liquid two-phase flow experiments to measure the flow signals by using the four-sector distributed conductance sensor. Then, we design a novel multitask-based temporal-channelwise convolutional neural network (MTCCNN) to predict the gas void fraction. In MTCCNN, we first utilize the decomposed convolutional block to extract temporal dependence and channel connection from fluid data. After further fusion by the dense layer, we apply multitask learning to make full use of the extracted features through both classification branch and gas void fraction prediction branch. We compare our MTCCNN with its variations to demonstrate the proposed improvements. We also present other competitive methods for comparisons, which shows that our MTCCNN presents a better performance in gas void fraction prediction.

Electroencephalography (EEG) decoding is an important part of Visual Evoked Potentials-based Brain-Computer Interfaces (BCIs), which directly determines the performance of BCIs. However, long-time attention to repetitive visual stimuli could cause physical and psychological fatigue, resulting in weaker reliable response and stronger noise interference, which exacerbates the difficulty of Visual Evoked Potentials EEG decoding. In this state, subjects' attention could not be concentrated enough and the frequency response of their brains becomes less reliable. To solve these problems, we propose an attention-based parallel multiscale convolutional neural network (AMS-CNN). Specifically, the AMS-CNN first extract robust temporal representations via two parallel convolutional layers with small and large temporal filters respectively. Then, we employ two sequential convolution blocks for spatial fusion and temporal fusion to extract advanced feature representations. Further, we use attention mechanism to weight the features at different moments according to the output-related interest. Finally, we employ a full connected layer with softmax activation function for classification. Two fatigue datasets collected from our lab are implemented to validate the superior classification performance of the proposed method compared to the state-of-the-art methods. Analysis reveals the competitiveness of multiscale convolution and attention mechanism. These results suggest that the proposed framework is a promising solution to improving the decoding performance of Visual Evoked Potential BCIs.

Real-world networks exhibit prominent hierarchical and modular structures, with various subgraphs as building blocks. Most existing studies simply consider distinct subgraphs as motifs and use only their numbers to characterize the underlying network. Although such statistics can be used to describe a network model, or even to design some network algorithms, the role of subgraphs in such applications can be further explored so as to improve the results. In this article, the concept of subgraph network (SGN) is introduced and then applied to network models, with algorithms designed for constructing the 1st-order and 2nd-order SGNs, which can be easily extended to build higher-order ones. Furthermore, these SGNs are used to expand the structural feature space of the underlying network, beneficial for network classification. Numerical experiments demonstrate that the network classification model based on the structural features of the original network together with the 1st-order and 2nd-order SGNs always performs the best as compared to the models based only on one or two of such networks. In other words, the structural features of SGNs can complement that of the original network for better network classification, regardless of the feature extraction method used, such as the handcrafted, network embedding and kernel-based methods.

In social networks, by removing some target-sensitive links, privacy protection might be achieved. However, some hidden links can still be re-observed by link prediction methods on observable networks. In this paper, the conventional link prediction method named Resource Allocation Index (RA) is adopted for privacy attacks. Several defense methods are proposed, including heuristic and evolutionary approaches, to protect targeted links from RA attack. In particular, incremental computation is proposed for accelerating the calculation of fitness in evolutionary approaches. This is the first time to study privacy protection for targeted links against similarity based link prediction attacks. Some links are randomly selected from original network as targeted links for experimentation. The experimental results on nine real-world networks demonstrate the superiority of the evolutionary perturbations, especially EDA, for defending against RA attack. Moreover, experimental results show that the proposed perturbation generated by EDA is transferable and can even defend against other link prediction attacks which are based on high order similarity between pairwise nodes, although it is designed to prevent RA attack.

While neural adaptive control is widely used for dealing with continuous- or discrete-time dynamical systems, less is known about its mechanism and performance in hybrid dynamical systems. This article develops analytical tools to investigate the neural adaptive tracking control of the hybrid Markovian switching networks with heterogeneous nonlinear dynamics and randomly switched topologies. A gradient-descent adaptation law built on neural networks (NNs) is presented for efficient distributed adaptive control. It is shown that the proposed control scheme can guarantee a stable closed-loop error system for any positive control gain and tuning gain. The tracking error is demonstrated to be practically uniformly exponentially stable with a threshold in the mean-square sense. This study further reveals how the topological structure affects the NN function, by measuring the influence of the switched topologies on the learning performance.

Brain–computer interface (BCI) systems based on electroencephalography (EEG) signals have been extensively used in medical practice. To enhance the BCI performance, improving the classification accuracy of EEG signals is the key, which has always been the focus of research and development. In this article, a novel method integrating complex network and broad learning system (BLS) is proposed for visual evoked potential (VEP)-based BCI research. First, systematic VEP-based brain experiments are conducted for obtaining EEG signals, including steady-state VEP (SSVEP) and steady-state motion VEP (SSMVEP). Then, limited penetrable visibility graph (LPVG) and its degree sequence are employed to implement the preliminary feature extraction. All these features are finally fed into a BLS to study and classify the SSVEP and SSMVEP signals, respectively. The classification results show that our LPVG-based BLS can effectively classify VEP-based EEG signals, with average classification accuracy 96.22% for SSVEP and 74.54% for SSMVEP. These results are significantly better than other comparison methods as well as traditional CCA-based methods. All these open up new venues for studying EEG-based BCI systems via the fusion of network science and BLS.

The minimal real part of all the nonzero eigenvalues of Laplacian matrix, also known as the dominant convergence rate, characterizes the consensus performance of multiagent systems on a directed graph. The effect of adding the second reverse edge to a directed chain graph on the dominant convergence rate is investigated. According to the relative positions of the two reverse edges, three cases are discussed, respectively. It is revealed that the dominant convergence rate of the whole network is determined only by the ranges and the relative positions of the reverse edges. Moreover, the consensus performance will not get better with the new reverse edge being added, and it decreases as the reverse range increases. Finally, the theoretical results are illustrated by some numerical examples.

Pinning control of a complex network aims at forcing the states of all nodes to track an external signal by controlling a small number of nodes in the network. In this paper, an algebraic graph-theoretic condition is introduced to optimize pinning control. When individual node dynamics and coupling strength of the network are given, the effectiveness of pinning scheme can be measured by the smallest eigenvalue of the grounded Laplacian matrix obtained by deleting the rows and columns corresponding to the pinned nodes from the Laplacian matrix of the network. The larger this smallest eigenvalue, the more effective the pinning scheme. Spectral properties of the smallest eigenvalue are analyzed using the network topology information, including the spectrum of the network Laplacian matrix, the minimal degree of uncontrolled nodes, the number of edges between the controlled node set and the uncontrolled node set, etc. The identified properties are shown effective for optimizing the pinning control strategy, as demonstrated by illustrative examples. Finally, for both scale-free and small-world networks, in order to maximize their corresponding smallest eigenvalues, it is better to pin the nodes with large degrees when the percentage of pinned nodes is relatively small, while it is better to pin nodes with small degrees when the percentage is relatively large. This surprising phenomenon can be explained by one of the theorems established.

In this paper, we focus on designing a high-data-rate noncoherent chaotic communication scheme to satisfy the demand of the explosive growth in data traffic. To achieve this goal, a joint time-frequency index modulation assisted multiple-mode DCSK (JTFIM-MM-DCSK) system is proposed, where a pair of distinguished signal modes are modulated into the selected subcarriers and another signal mode is transmitted by the unselected subcarriers. In this configuration, besides the modulated bits used for physical transmission, the carrier index bits and time slot index bits, conveyed by the state of whether subcarriers and time slots are selected or not, are also transmitted implicitly to achieve higher data rate. Moreover, the design of multiple-mode signals ensures that it is taking full advantage of all subcarriers and time slots to transmit the information bits, thereby improving the data rate significantly. The bit error rate (BER) expressions of the JTFIM-MM-DCSK system are derived over additive white Gaussian noise (AWGN) and multipath Rayleigh fading channels, which are checked by computer simulations. Finally, the advantage of the JTFIM-MM-DCSK system over other up-to-date noncoherent chaotic communication systems is demonstrated in terms of BER performance through extensive computer simulations.

The issue of opinion sharing and formation has received considerable attention in the academic literature, and a few models have been proposed to study this problem. However, existing models are limited to the interactions among nearest neighbors, ignoring those second, third, and higher-order neighbors, despite the fact that higher-order interactions occur frequently in real social networks. In this paper, we develop a new model for opinion dynamics by incorporating long-range interactions based on higher-order random walks. We prove that the model converges to a fixed opinion vector, which may differ greatly from those models without higher-order interactions. Since direct computation of the equilibrium opinions is computationally expensive, which involves the operations of huge-scale matrix multiplication and inversion, we design a theoretically convergence-guaranteed estimation algorithm that approximates the equilibrium opinion vector nearly linearly in both space and time with respect to the number of edges in the graph. We conduct extensive experiments on various social networks, demonstrating that the new algorithm is both highly efficient and effective.

This paper proposes a new model and its analysis results for time-varying structurally balanced networks. Through model transformations, the system stability problem is converted into the problem of product convergence of infinite sub-stochastic matrices (PCISM). Further, by constructing a new digraph for each interaction topology, the problem of PCISM can be handled by virtue of the properties of row-stochastic matrices. When all leaders belong to only one of the two subgroups, it is shown that the followers that are in the same subgroup as the leaders gradually enter the convex hull formed by the leaders' states, while the others gradually enter the convex hull formed by the leaders' sign-inverted states. And when both subgroups contain leaders, a sufficient algebraic graph condition is established to ensure that all followers can enter the convex hull consisting of the leaders' states and sign-inverted states together. Moreover, it is also found that the followers keep active after entering the convex hulls. Finally, the bipartite containment performance is verified by a simulation test.

This technical note presents some new and explicit stability results for Volterra systems using two different approaches. The first approach is based on monomial domination of the Volterra system's memoryless output nonlinearity and the second on its Lipschitz-norm. The former yields more widely applicable results, but introduces nonconvexity in the signal spaces to be dealt with for certain parameter values.

The objective of this paper is to design the protocols with a final consensus value and settling time estimations for finite-time consensus of multiagent systems. A couple of new edge-based protocols are developed for multiple second-order nonlinear agents under bounded or Lipschitz-type nonlinear functions, respectively. The final consensus value of the multiagent system is obtained as an average expression. Further, to obtain the estimation of the finite settling time, a special Lyapunov function is constructed. Through the construction processes, both the final consensus value and the settling time are obtained. Finally, as applications, a finite-time formation controller based on the first protocol is designed for multiple mini-spacecraft, verified by simulations.

A distributed nonsmooth convex optimization problem subject to a general type of constraint, including equality and inequality as well as bounded constraints, is studied in this paper for a multiagent network with a fixed and connected communication topology. To collectively solve such a complex optimization problem, primal-dual dynamics with projection operation are investigated under optimal conditions. For the nonsmooth convex optimization problem, a framework under the LaSalle's invariance principle from nonsmooth analysis is established, where the asymptotic stability of the primal-dual dynamics at an optimal solution is guaranteed. For the case where inequality and bounded constraints are not involved and the objective function is twice differentiable and strongly convex, the globally exponential convergence of the primal-dual dynamics is established. Finally, two simulations are provided to verify and visualize the theoretical results.

While the majority of methods for community detection produce disjoint communities of nodes, most real-world networks naturally involve overlapping communities. In this paper, a scalable method for the detection of overlapping communities in large networks is proposed. The method is based on an extension of the notion of normalized cut to cope with overlapping communities. A spectral clustering algorithm is formulated to solve the related cut minimization problem. When available, the algorithm may take into account prior information about the likelihood for each node to belong to several communities. This information can either be extracted from the available metadata or from node centrality measures. We also introduce a hierarchical version of the algorithm to automatically detect the number of communities. In addition, a new benchmark model extending the stochastic blockmodel for graphs with overlapping communities is formulated. Our experiments show that the proposed spectral method outperforms the state-of-the-art algorithms in terms of computational complexity and accuracy on our benchmark graph model and on five real-world networks, including a lexical network and large-scale social networks. The scalability of the proposed algorithm is also demonstrated on large synthetic graphs with millions of nodes and edges.

A new approach for trajectory tracking on uncertain complex networks is proposed. To achieve this goal, a neural controller is applied to a small fraction of nodes (pinned ones). Such controller is composed of an on-line identifier based on a recurrent high-order neural network, and an inverse optimal controller to track the desired trajectory; a complete stability analysis is also included. In order to verify the applicability and good performance of the proposed control scheme, a representative example is simulated, which consists of a complex network with each node described by a chaotic Lorenz oscillator.

Effective supply chain management is a crucial competency for modern enterprises, but the issue has not been systemically addressed. To this end, we develop a distributed model predictive control (DMPC) approach with minimal information exchange and communication to handle supply chain operations and management. Therein, each decision maker relies on an agent with local information and they are collaborating to minimize a global cost function that measures the control performance of the entire network. The information flow topology is utilized to sequentially solve the DMPC optimization problem. The control sequence of downstream nodes is predicted with information transmitted to the upstream nodes. The stability of the proposed DMPC scheme is provably guaranteed. Finally, a numerical example is presented to verify the effectiveness of the proposed scheme.

Aiming to solve the cluster lag consensus (CLC) problem of networked nonlinear agents with a switching topologies, this paper proposes a control algorithm based on the measurements of position and velocity. When the network has several clusters of agents, under the conditions that each cluster is a strongly connected digraph including isolated agents, and at least one agent in each cluster can communicate with the common leader each time, a sufficient condition is derived for reaching CLC. Finally, a numerical simulation is demonstrated to validate the proposed control algorithm and the developed conditions.

In this paper, the global pinning synchronization problem is studied for a complex dynamical network to follow a dynamic target system. A distinguished feature of the present network model is that the target system may have some predesigned control inputs. This implies that, when pinning synchronization is guaranteed, the states of the nodes within such a pinning-controlled dynamical network may approach a specified trajectory which does not satisfy the system equation of the uncoupling individual node system within the network. The practical constraint that the external control inputs acting on the target system are unknown to any node in the considered network poses a big challenge in solving such a pinning synchronization problem. The designed scheme for achieving pinning synchronization is executed in two steps. Specifically, the first step is to select some nodes to pin such that the augmented interaction topology has at least one directed spanning tree rooted at the node describing the target system, while the second step is to construct a coupling law to synchronize all the states of nodes within the network. Moreover, two kinds of discontinuous coupling laws with static and adaptive coupling gains are, respectively, proposed to achieve pinning synchronization. Meanwhile, by utilizing nonsingular ${M}$ -matrix theory and Lyapunov stability analysis for nonsmooth system, some efficient criteria are established for guaranteeing synchronization in the pinning-controlled networks. Numerical simulations on pinning synchronization of networking Chua's circuit systems are finally given to verify the analytic results.

Restart strategy helps the covariance matrix adaptation evolution strategy (CMA-ES) to increase the probability of finding the global optimum in optimization, while a single run CMA-ES is easy to be trapped in local optima. In this paper, the continuous non-revisiting genetic algorithm (cNrGA) is used to help CMA-ES to achieve multiple restarts from different sub-regions of the search space. The CMA-ES with on-line search history-assisted restart strategy (HR-CMA-ES) is proposed. The entire on-line search history of cNrGA is stored in a binary space partitioning (BSP) tree, which is effective for performing local search. The frequently sampled sub-region is reflected by a deep position in the BSP tree. When leaf nodes are located deeper than a threshold, the corresponding sub-region is considered a region of interest (ROI). In HR-CMA-ES, cNrGA is responsible for global exploration and suggesting ROI for CMA-ES to perform an exploitation within or around the ROI. CMA-ES restarts independently in each suggested ROI. The non-revisiting mechanism of cNrGA avoids to suggest the same ROI for a second time. Experimental results on the CEC 2013 and 2017 benchmark suites show that HR-CMA-ES performs better than both CMA-ES and cNrGA. A positive synergy is observed by the memetic cooperation of the two algorithms.

When implemented in the digital domain with time, space and value discretized in the binary form, many good dynamical properties of chaotic systems in continuous domain may be degraded or even diminish. To measure the dynamic complexity of a digital chaotic system, the dynamics can be transformed to the form of a state-mapping network. Then, the parameters of the network are verified by some typical dynamical metrics of the original chaotic system in infinite precision, such as Lyapunov exponent and entropy. This article reviews some representative works on the network-based analysis of digital chaotic dynamics and presents a general framework for such analysis, unveiling some intrinsic relationships between digital chaos and complex networks. As an example for discussion, the dynamics of a state-mapping network of the Logistic map in a fixed-precision computer is analyzed and discussed.

In this paper, a distributed average tracking (DAT) problem is studied for Lipschitz-type of nonlinear dynamical systems. The objective is to design DAT algorithms for locally interactive agents to track the average of multiple reference signals. Here, in both dynamics of agents and reference signals, there is a nonlinear term satisfying a Lipschitz-type condition. Three types of DAT algorithms are designed. First, based on state-dependent-gain design principles, a robust DAT algorithm is developed for solving DAT problems without requiring the same initial condition. Second, by using a gain adaption scheme, an adaptive DAT algorithm is designed to remove the requirement that global information, such as the eigenvalue of the Laplacian and the Lipschitz constant, is known to all agents. Third, to reduce chattering and make the algorithms easier to implement, a couple of continuous DAT algorithms based on time-varying or time-invariant boundary layers are designed, respectively, as a continuous approximation of the aforementioned discontinuous DAT algorithms. Finally, some simulation examples are presented to verify the proposed DAT algorithms.

Due to the inherent disturbances associated with flow structures, measurement of the complicated flow parameters in multiphase flows remains a challenging problem of significant importance. The flow dynamical behaviors are still elusive. In this paper, a multichannel complex impedance measurement system is designed to cope with this difficult issue. First, the geometry of the distributed multielectrode impedance sensor is optimized and a matched hardware measurement system is developed. After performance evaluation, a convolutional neural network and long short-term memory based measurement model is formulated for measuring flow parameters with high accuracy. The mean absolute error is only 0.36% for water cut and 0.77% for total flow velocity. Further, from the perspective of Lempel-Ziv complexity and mutual information, the relationship between the diverse flow structures and spatial flow behaviors is explored, leading to a deeper understanding of oil-water flows. All the experimental and analytical results demonstrate that the combination of deep learning and the designed impedance sensor measurement system allows measuring the complicated flow parameters, thereby characterizing the flow structures and behaviors. This opens up a new venue for exploring industrial multiphase flows and serving for an efficient oilfield exploitation as well.

The important topic of multistability of continuous-and discrete-time neural network (NN) models has been investigated rather extensively. Concerning the design of associative memories, multistability of delayed hybrid NNs is studied in this paper with an emphasis on the impulse effects. Arising from the spiking phenomenon in biological networks, impulsive NNs provide an efficient model for synaptic interconnections among neurons. Using state-space decomposition, the coexistence of multiple equilibria of hybrid impulsive NNs is analyzed. Multistability criteria are then established regrading delayed hybrid impulsive neurodynamics, for which both the impulse effects on the convergence rate and the basins of attraction of the equilibria are discussed. Illustrative examples are given to verify the theoretical results and demonstrate an application to the design of associative memories. It is shown by an experimental example that delayed hybrid impulsive NNs have the advantages of high storage capacity and high fault tolerance when used for associative memories.

This paper is concerned with quasi-synchronization of delayed memristive neural networks (MNNs) with switching jumps mismatches via aperiodically intermittent control. The issue is presented for three reasons: 1) the existing controllers for synchronization may be too complicated and not economical; 2) under the influence of switching jumps mismatches, synchronization of MNNs may fail to achieve; and 3) matrix measure method is less conservative but cannot be applied directly to synchronization of MNNs. To overcome these difficulties, the concept of asynchronously switching time interval is proposed to describe the phenomenon when the drive-response MNNs switch their connection weights asynchronously. Then, aperiodically intermittent control is designed and quasi-synchronization analysis is carried out based on a combined method that compromises the merits of interval matrix method and matrix measure method. A quasi-synchronization criterion, expressed in terms of the mixture of p-norm and matrix measure of the memristive connection weights, is established. Meanwhile, the fundamental reason for the failure of complete synchronization is revealed. Moreover, an explicit expression of the error level is obtained and the design of the controller under a predetermined error level is presented. The obtained results in this paper reduce the conservativeness and provide a novel insight into the research of synchronization of MNNs.

In this paper, finite-time consensus problem is considered for a class of second-order multi-agent systems with a directed communication topology. A fully-distributed control protocol is proposed for solving the finite-time consensus problem, without using any global information. A simulation example is presented to verify the theoretical result and to show the effectiveness of the protocol.

In this study, two generalised carrier index M ‐ary differential chaos shift keying (CI‐MDCSK) schemes are proposed, which combine index modulation with multicarrier M ‐ary DCSK (MC‐MDCSK). At the transmitter, two different index selectors based on two different mapping rulers are employed to select active carriers, where the modulated bits are transmitted by the active carriers through M ‐ary DCSK modulation, which is based on the Hilbert transform and constellation theory. At receiver, maximum or minimum energy detection is employed to determine the active carriers, where the bits carried on these active carriers are demodulated. The analytical bit error rate (BER) expressions over additive white Gaussian noise as well as multipath Rayleigh fading channels are derived. Simulations are performed with different numbers of carriers and different constellation sizes. Both analytical and simulation results show the superiority of the new schemes in BER performance or spectral efficiency (SE) compared with the MC‐MDCSK scheme. Moreover, compared with conventional DCSK, CI‐MDCSK schemes owns both better BER performance and SE in some cases, where the constellation is not greater than 8.

Coded modulation (CM) is a bandwidth efficient framework to approach the capacity limit of the differential chaos shift keying (DCSK) systems. In this paper, we propose an M-ary DCSK system operated with CM based on nonbinary protograph low-density parity-check (LDPC) codes over Rayleigh fading channels. First, we investigate the performance of the proposed nonbinary channel coded DCSK (CM-DCSK) and bit-interleaved coded DCSK (BICM-DCSK). In particular, we show that CM-DCSK outperforms BICM-DCSK over Rayleigh fading channels in terms of capacity limit. Compared with BICM-DCSK, CM-DCSK can simplify the receiver structure, since it does not require turbo iteration between the noncoherent detector and channel decoder. Second, guided by the modified extrinsic information transfer (EXIT) analysis, we put forth two new types of nonbinary protograph LDPC codes to approach the capacity limit of CM-DCSK. Both EXIT analysis and simulation results demonstrate that the proposed protograph-coded CM-DCSK achieves a better error performance than BICM-DCSK even with iterative decoding. Furthermore, we show the performance superiority of nonbinary protograph-coded CM-DCSK over a practical ultra-wideband channel. Hence, we conclude that this proposed scheme offers a good alternative for wireless local area network applications.

This paper initiates a systematic methodology for real-time chaos-based video encryption and decryption communications on the system design and algorithm analysis. The proposed system design and algorithm analysis have been validated on an FPGA hardware platform via Verilog Hardware Description Language (Verilog HDL). Based on the fundamental anti-control principles of dynamical systems, a 6-D real domain chaotic system is designed, and then the corresponding Verilog HDL algorithm is developed. The proposed Verilog HDL algorithm is utilized to design a real-time chaos-based secure video communication system, with a generalized design principle derived, which is implemented on an FPGA hardware platform equipped with an XUP Virtex-II chip. Following this line, the designed working mechanism is demonstrated by hardware experiments. The security performance is tested using the TESTU01 statistical test suites, the differential analysis, and the sensitivity of key parameters mismatch. Both theoretical analysis and experimental results validate the feasibility and reliability of the proposed system.

The coexistence of multiple types of interactions within social, technological, and biological networks has motivated the study of the multilayer nature of real-world networks. Meanwhile, identifying network structures from dynamical observations is an essential issue pervading over the current research on complex networks. This paper addresses the problem of structure identification for multilayer networks, which is an important topic but involves a challenging inverse problem. To clearly reveal the formalism, the simplest two-layer network model is considered and a new approach to identifying the structure of one layer is proposed. Specifically, if the interested layer is sparsely connected and the node behaviors of the other layer are observable at a few time points, then a theoretical framework is established based on compressive sensing and regularization. Some numerical examples illustrate the effectiveness of the identification scheme, its requirement of a relatively small number of observations, as well as its robustness against small noise. It is noteworthy that the framework can be straightforwardly extended to multilayer networks, thus applicable to a variety of real-world complex systems.

In this paper, the problem of non-negative edge consensus of undirected networked linear time-invariant systems is addressed by associating each edge of the network with a state variable, for which a distributed algorithm is constructed. Sufficient conditions referring only to the number of edges are derived for non-negative edge consensus of the networked systems. Subsequently, the linear programming method and a low-gain feedback technique are introduced to simplify the design of the feedback gain matrix for achieving the non-negative edge consensus. It is found that the low-gain feedback technique has a good effect on the non-negative edge consensus of the networked systems subject to input saturation. Numerical simulations are presented to verify the effectiveness of the theoretical results.

Neural networks (NNs) have emerged as a powerful illustrative diagram for the brain. Unveiling the mechanism of neural-dynamic evolution is one of the crucial steps toward understanding how the brain works and evolves. Inspired by the universal existence of impulses in many real systems, this paper formulates a type of hybrid NNs (HNNs) with impulses, time delays, and interval uncertainties, and studies its global dynamic evolution by a robust interval analysis. The HNNs incorporate both continuous-time implementation and impulsive jump in mutual activations, where time delays and interval uncertainties are represented simultaneously. By constructing a Banach contraction mapping, the existence and uniqueness of the equilibrium of the HNN model are proved and analyzed in detail. Based on nonsmooth Lyapunov functions and delayed impulsive differential equations, new criteria are derived for ensuring the global robust exponential stability of the HNNs. Convergence analysis together with illustrative examples show the effectiveness of the theoretical results.

In this paper, the swarming behavior of multiple Euler-Lagrange systems with cooperation-competition interactions is investigated, where the agents can cooperate or compete with each other and the parameters of the systems are uncertain. The distributed stabilization problem is first studied, by introducing an auxiliary system to each agent, where the common assumption that the cooperation-competition network satisfies the digon sign-symmetry condition is removed. Based on the input-output property of the auxiliary system, it is found that distributed stabilization can be achieved provided that the cooperation subnetwork is strongly connected and the parameters of the auxiliary system are chosen appropriately. Furthermore, as an extension, a distributed consensus tracking problem of the considered multiagent systems is discussed, where the concept of equi-competition is introduced and a new pinning control strategy is proposed based on the designed auxiliary system. Finally, illustrative examples are provided to show the effectiveness of the theoretical analysis.

In order to avoid congestion in the second-order nonlinear leader-following multiagent systems over capacity-limited paths, an approach called cluster lag consensus is proposed, which means that the agents in different clusters will pass through the same positions with the same velocities but lag behind the leader at different times. Lyapunov functionals and matrix theory are applied to analyze such cluster lag consensus. It is shown that when the graphic roots of clusters are influenced by the leader and the intracoupling of cluster agents is larger than a threshold, the cluster lag consensus can be achieved. Furthermore, the cluster lag consensus with a time-varying communication topology is investigated. Finally, an illustrative example is presented to demonstrate the effectiveness of the theoretical results. In particular, when the physical sizes of the agents are taken into consideration, it is shown that with a rearrangement and a position transformation, the multiagent system will reach cluster lag consensus in the new coordinate system. This means that all agents in the same cluster will reach consensus on the velocity, but their positions may be different and yet their relative positions converge to a constant asymptotically.

In this paper, the stability problem of formation of multi-agents subject to failures in their communication links is addressed. The objective of the formation control problem is to maintain the inter-agent distances to be constants over time using a distributed control algorithm implemented in each agent. Previous research results showed that a distributed gradient-based control can locally asymptotically stabilize an undirected formation. However, in the case of failures in the inter-agent communication network, the degrees of freedom for some nodes might become uncontrollable and, consequently, the formation starts deviating from the desired conditions due to uncertainties and noise. In this paper, it is proved that in a faulty formation system, if there still exists a path between the agents on the both sides of the failed link, the gradient-based control signal can recover the formation without adding any new link to the network. Based on this feature, an algorithm for recovering the formation from the fault is developed. Simulation results show that the proposed recovery algorithm can tolerate small values of delays in data communications.

Social networks have become one of the most important research platforms in the big data era. Modelling social networks enables researchers and engineers to understand and analyze their intrinsic properties thereby implementing their real applications. A number of studies on social network modelling focus on a few characteristics, such as the number of edges (i.e., two-star motifs), scale-free degree distribution, and assortative property. This paper proposes an exponential triangle model for a typical social network, namely the Facebook network, established based on big data, and further analyzes its primary attributes of common interest on topological features. This new model has a power-law node-degree distribution with a flat top and an exponential cut-off tail, in remarkable agreement with one large-scale Facebook dataset. It can be used to predict future links of the Facebook network and help improve the friend-recommendation system. Furthermore, this work provides a useful graph-theoretic tool for Facebook network studies and enhances potential applications of social networks in general.

This paper applies a recurrent higher-order neural network for sliding-mode pinning control of complex networks for achieving trajectory tracking. This control strategy does not require having the same coupling strength for all node connections on the network. The tracking effectiveness and dynamical behavior of the controlled network is illustrated via simulations.

In this paper, a novel differential chaotic bit-interleaved coded modulation (DC-BICM) system is proposed for band-limited transmission. This system combines protograph-based low density parity check codes with constellation-based M-ary differential chaos shift keying (DCSK) modulation by one bitwise interleaving. Bit error rate simulation results show that the system has higher coding gain compared with the constellation-based M-ary DCSK modulation system with the same spectral efficiency over multipath Rayleigh fading channels. At the same time, several simulations and P-EXIT analysis are used to analyze the performance of the proposed system. It is found that there is a lot of room for optimization of the system by comparing decoding thresholds and simulation results. Moreover, the system with only partial channel state information has better performance and lower complexity compared with the traditional bit-interleaved coded modulation (BICM) directsequence-spread-spectrum system. As a result, the DC-BICM system is a good candidate for band-limited transmission.

Lag consensus means that the corresponding state vectors of the followers are behind the leader with a lag time. In this paper, Lyapunov functional and matrix theory are applied to analyze pinning-controlled lag consensus of second-order nonlinear multiagent systems. The focus is twofold: 1) to find out which agents should be pinned and 2) to determine what the coupling strength should be, so that the multiagent systems can reach lag consensus. Moreover, the practical problem in a noisy environment is considered. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed pinning control protocol.

This paper studies the dynamics of multiagent systems with a multilayer structure, proposing a novel layered event-triggered scheme (LETS) for consensus. This LETS emphasizes on synchronous information transmission in the same layer but asynchronous message update between different layers, which differs from the existing centralized or distributed event-triggered schemes. Moreover, under the LETS, agents in different layers achieve asymptotical consensus eventually and the Zeno behavior is successfully eliminated. Furthermore, an algorithm is provided to avoid continuous event detection, verified by a numerical example.

By employing the finite-time control method, the consensus control algorithm for higher-order multiagent systems is designed in this paper. Under a neighbor-based rule, a higher-order finite-time consensus algorithm is explicitly constructed, which only uses local information. The finite-time consensus control algorithm can guarantee that the state consensus is achieved in a finite time. In addition, for multiagent systems having a leader-following structure, the consensus algorithm is also designed. Finally, two examples are presented to show the effectiveness.

This paper is concerned with the synchronization of multiagent systems connected via different types of interactions, known as multilayer networks. Additive coupling and Markovian switching coupling are proposed to capture the layered connections with two kinds of mathematical models constructed. First, based on simultaneously diagonalization of multiple Laplacian matrices, a general criterion is derived, ensuring that the synchronization problem with additive coupling can be decoupled. Then, an alternative condition is presented, which is related to the number of layers, regardless of the number of agents. With the derived criteria, a concept of joint synchronization region is introduced and further discussed as a network design problem. Synchronization with Markovian switching layers is also analyzed in parallel, exemplified by some special cases of two-layer networks. Finally, a group of cellular neural networks coupled by two-layer connections are chosen to illustrate the effectiveness of the theoretical results.

Capacity bounds are calculated for the differential chaos shift keying (DCSK) system with non‐coherent detectors, including differentially coherent detector and energy detector, over additive white Gaussian noise (AWGN) and Rayleigh fading channels. Through theoretical analysis and numerical simulations, it is found that the capacity characteristics of the non‐coherent DCSK system are significantly different from those of the coherent case. It is shown that there are different capacity bounds corresponding to different spreading factor values. Optimal code rates are found, which minimise the required bit signal‐to‐noise ratio for a reliable communication system, and they are increasing with the increase of the spreading factor value over an AWGN channel while decreasing over a Rayleigh fading channel. As compared with the AWGN channel, the performance over a Rayleigh fading channel is much more sensitive to the code rate. The new results are useful as benchmark for designing capacity‐approaching codes for the non‐coherent DCSK system.

A compound control strategy is proposed for frequency regulation of source-grid-load systems in which power sources, power grids, and loads are all participating in the process. Here, power sources are conventional thermal generators, including new energy power generations, and loads are composed of energy storage units (ESUs) and grid-friendly appliances (GFAs). The proposed control scheme includes two levels of operations, with the upper level to be a model predictive control (MPC) for generators and the lower level to be a distributed leader-following consensus control strategy for multiple ESUs. For new energy power generations, the power outputs are restricted on a constant value during a sampling period based on a predicted generating curve. GFAs respond to the system frequency by regulating their active power consumption. Simulations on a single power system and three interconnected area power systems are provided to verify the effectiveness of the proposed compound control strategy.

In this paper, we study the problem of finite-time consensus of multiagent systems on a fixed directed interaction graph with a new protocol. Existing finite-time consensus protocols can be divided into two types: 1) continuous and 2) discontinuous, which were studied separately in the past. In this paper, we deal with both continuous and discontinuous protocols simultaneously, and design a centralized switching consensus protocol such that the finite-time consensus can be realized in a fast speed. The switching protocol depends on the range of the initial disagreement of the agents, for which we derive an exact bound to indicate at what time a continuous or a discontinuous protocol should be selected to use. Finally, we provide two numerical examples to illustrate the superiority of the proposed protocol and design method.

In this paper, we study the first-order consensus algorithm in the small-world Farey graph where agents are driven by white noise, aiming to unveil the effect of small-world topology on the robustness of the consensus algorithm. We characterize the coherence of the Farey graph in terms of the |$H_2$|-norm of the system, the square of which equals the steady-state variance and thus captures how closely agents track the consensus value. Based on the particular network structure, we derive an exact expression for the coherence in the Farey graph, whose dominant behavior scales logarithmically with the system size. To uncover the role of small-world topology, we also derive an analytical solution for the coherence of first-order consensus in the regular ring lattice sharing the same average degree as the Farey graph, whose dominant term grows linearly with the system size, implying that the small-world structure strongly affects the performance of the consensus algorithm.

Although the performance of a differential chaos shift keying (DCSK) system can be improved by designing appropriate channel codes, it is still a great challenge to do so for various channel models through transmitter and receiver designs, particularly with short frame length transmissions. Alternatively, to bypass the difficult task of designing a good channel code, an iterative receiver (IR) DCSK system is proposed in this paper. A soft demapper suitable for non-coherent M-ary DCSK system is presented, which can work either with or without fading amplitude information. Bit error rate (BER) performance shows its advantages over the non-IR DCSK system in different channel models. The achievable rate curves also indicate that gains relative to non-iterative DCSK system can be achieved with the iterative receiver.

A systematic methodology is proposed for a chaotic map-based real-time video encryption and decryption system with advanced Reduced Instruction Set Computer machine (ARM)-embedded hardware implementation. According to the anticontrol principle of dynamical systems, first, an 8-D discrete-time chaotic map-based system is constructed, which possesses the required property of 1-1 surjection in the integer range$[{0,\,N-1}]$, where$N$is the number of frame pixels, suitable for position scrambling of each video frame. Then, an 8-D discrete-time hyperchaotic system is designed for encryption–decryption of red, green, and blue (RGB) tricolor pixel values. Using the ARM-embedded platform super4412 model with Cortex-A9 processor, together with the standard QT cross-platform, an integrated chaotic map-based real-time secure video communication system is designed, implemented, and evaluated. In addition, the security performance of the designed system is tested using criteria from the National Institute of Standards and Technology statistical test suite. The main feature of this method is that, both scrambling–antiscrambling of RGB tricolor pixel positions and encryption–decryption of pixel values are realized simultaneously for enhancing the security. As is well known, compared with numerical simulations, hardware implementation for such a secure video communication system is very difficult to achieve, but we successfully implemented and tested in a real-world network environment. Both theoretical analysis and experimental results validate the feasibility and real-time performance of the new secure video communication system.

A new multiresolution M-ary differential chaos shift keying (DCSK) modulation scheme is proposed in this paper. It is a promising technique for providing a different quality of service for transmitted bits within a symbol according to their different bit error rate (BER) requirements based on the principle of nonuniformly spaced constellations. The new system not only is simple but also provides better antimultipath fading performance against various spreading factors, inheriting the advantages of the conventional DCSK system. Furthermore, the proposed scheme and its multicarrier version further increase spectral efficiency and use lower energy consumption at the same bandwidth as compared with the conventional DCSK and its multicarrier system. Explicit BER expressions of the new system are derived and analyzed over additive white Gaussian noise and multipath Rayleigh fading channels. All simulation results verify the prominent advantages of the new scheme and the accuracy of the new analytical approach.

In this paper1, we propose a novel cooperative scheme to enhance the performance of multiple-access (MA) differential-chaos-shift-keying (DCSK) systems. We provide the bit-error-rate (BER) performance and throughput analyses for the new system with a decode-and-forward (DF) protocol over Nakagami-m fading channels. Our simulated results not only show that this system significantly improves the BER performance as compared to the existing DCSK non-cooperative (DCSK-NC) system and the multiple-input multiple-output DCSK (MIMO-DCSK) system, but also verify the theoretical analyses. Furthermore, we show that the throughput of this system approximately equals that of the DCSK-NC system, both of which have prominent improvements over the MIMO-DCSK system. We thus believe that the proposed system can be a good framework for chaos-modulation-based wireless communications.

Over the last decade, complex networks have emerged to be a promising research field in the area of circuits and systems. This mini-review paper introduces the special session that deals with theory and applications of complex networks and provides brief review of their advances and challenges. The paper further promotes some important research topics in the field with emphasis on the multidisciplinary research interests.

In this brief, we investigate pinning control for cluster synchronization of undirected complex dynamical networks using a decentralized adaptive strategy. Unlike most existing pinning-control algorithms with or without an adaptive strategy, which require global information of the underlying network such as the eigenvalues of the coupling matrix of the whole network or a centralized adaptive control scheme, we propose a novel decentralized adaptive pinning-control scheme for cluster synchronization of undirected networks using a local adaptive strategy on both coupling strengths and feedback gains. By introducing this local adaptive strategy on each node, we show that the network can synchronize using weak coupling strengths and small feedback gains. Finally, we present some simulations to verify and illustrate the theoretical results.

This paper reviews some main results and progress in distributed multi-agent coordination, focusing on papers published in major control systems and robotics journals since 2006. Distributed coordination of multiple vehicles, including unmanned aerial vehicles, unmanned ground vehicles, and unmanned underwater vehicles, has been a very active research subject studied extensively by the systems and control community. The recent results in this area are categorized into several directions, such as consensus, formation control, optimization, and estimation. After the review, a short discussion section is included to summarize the existing research and to propose several promising research directions along with some open problems that are deemed important for further investigations.

This paper addresses an on-line approximation-based robust adaptive control problem for the automatic train operation (ATO) system under actuator saturation caused by constraints from serving motors. A robust adaptive control law is proposed, which is proved capable of on-line estimating of the unknown system parameters and stabilizing the closed-loop system. To cope with actuator saturation, another robust adaptive control is proposed for the ATO system, by explicitly considering the actuator saturation nonlinearity other than unknown system parameters, which is also proved capable of stabilizing the closed-loop system. Simulation results are presented to verify the effectiveness of the two proposed control laws.

This paper addresses the distributed consensus tracking problem for a class of multi-agent systems with Lipschitz-type node dynamics in the presence of a single leader. The main contribution in the present work is to solve the consensus tracking problem without the over-idealized assumption that the communication topology among dynamic agents is strongly connected and fixed. A distributed protocol based only on the relative states between neighboring agents is designed. Then, by using tools from nonnegative matrix analysis and switching systems theory, it is theoretically shown that consensus tracking in a closed-loop multi-agent network with a switching directed topology can be achieved if there always exists a directed path from the leader to each follower, with the control parameters suitably selected.

In this paper, we address routing in complex networks. Routing traffic across a network requires finding best possible paths between sources and destinations. When data traffic changes dynamically, a path that was optimal in the past may not be the best for the next packet. Adapting to traffic changes and finding optimal paths dynamically are challenging tasks. They become more demanding in large and complex networks. In optical burst switching (OBS) networks, two optical bursts contending for the same link need resolution mechanisms other than queueing. Deflection routing protocols are used to override routing tables and “deflect” one of the bursts to a free link. Instead of deflecting bursts at an immediate point of contention, the proposed Random Early Deflection (RED-f) routing protocol triggers deflection ahead of time and, thus, offers additional routing paths and lowers the burst loss rate due to contention. Simulations demonstrate that RED-f enabled nodes in a scale-free complex network reduce burst loss rate by exchanging control information with only few other network nodes.

Multi-agent systems are ubiquitous in the world. Recently, multi-agent systems have received increasing attention from mathematics, physics, engineering sciences, and social science communities. This paper firstly introduces several fundamental concepts and then reviews several representative models of multi-agent systems, including the Boids model, Vicsek model, Couzin-Levin model and its invariants, and various complex dynamical networks. Based on these models, it further investigates the dynamical behaviors of multi-agent systems, such as consensus, convergence, adaptation, and consensus decision-making. Moreover, it briefly reviews the main progress in the control of multi-agent systems. Finally, it looks ahead into some important research topics on multi-agent systems, with regard to modelling, analysis, and control.

Over the last two decades, multi-scroll chaos generation has seen promising advances and becomes an active research field. This paper initiates a novel approach to design various grid multi-wing butterfly chaotic attractors from piecewise Lü system based on switching control and heteroclinic orbit. It should be especially pointed out that these generating multi-wing chaotic attractors are chaotic in the sense of Smale horseshoe from Shilnikov theorem. Moreover, there are some potential engineering applications in the future because of the simplicity of the proposed design approach.

Designing a non-ideal delay line (DL) with phase distortion in a transmitted-reference ultra-wideband system with an autocorrelation receiver is a great technical challenge. Differing from the currently empirical design method of DL, a semi-analytic approach is proposed through Gaussian approximation of the expression for conditional bit error rate (BER), based on investigation on the degradation of average BER caused by a group delay ripple range (GDRR) over independent Nakagami-m fading channels. This GDRR-based design method can directly evaluate its effects on the system performance and determine the acceptable phase distortion level to trade-off the BER performance and system complexity.

The aim of this paper is to introduce the special session on Recent Advances in Complex Networks: Theories and Applications at ISCAS 2010 by giving a brief outline of the subject and presenting some recent advances in a field of our own interest, i.e., Control and Synchronization of Complex Networks, with special attention to adaptive synchronization and control strategies.

In this paper, we propose a decentralized adaptive pinning control scheme for synchronization of undirected networks using a local adaptive strategy to determine both coupling strengths and feedback gains. By applying this local adaptive strategy, we show that the network can achieve synchronization with small coupling strengths and feedback gains. We provide some simulations to verify and illustrate the theoretical results.

Frequency modulated differential chaos shift keying (DCSK/FM-DCSK), a joint modulation and spread spectrum technique, is a promising modulation technique for low-cost and low-complexity wireless transmission applications. The noise performance of DCSK/FM-DCSK is superior to most conventional modulation schemes in multipath-channel environment. Cooperative communication, on the other hand, is receiving increasing attention due to its efficiency in sharing single-antenna mobiles or network nodes with other antennas to achieve combating fading via transmitting diversity. By combining these two aspects of advantages, a novel chaotic communication system is proposed in this paper, aiming to achieve combating multipath and fading effects. Simulation results show that significant performance improvement can be achieved by the proposed system in comparison with non-cooperative systems. It is found that the choice of some key parameters, such as the spread spectrum factor and the relay selective strategy, affect the system performance prominently. It reveals that the combination of the DCSK/FM-DCSK framework with a cooperative strategy is of great practical value for certain wireless communication networks.

In this study, the performance of the frequency-modulated differential chaos shift keying (FM-DCSK) ultra-wideband (UWB) system is evaluated through two important system parameters, the guard interval and the integration interval of the integrator, over indoor communication channels. It is found that the existing FM-DCSK UWB system suffers severe performance degradation in the IEEE 802.15.4a low-rate application. To resolve this problem, a new optimising scheme for the integration interval is presented. Simulation results show that the performance of the proposed scheme is significantly improved and becomes insensitive to the data rate. In addition, some notable advantages are evident in the proposed system, such as moderate multiple-access capability and feasible cross-layer optimisation.

In this letter, a novel recurrent neural network based on the gradient method is proposed for solving linear programming problems. Finite-time convergence of the proposed neural network is proved by using the Lyapunov method. Compared with the existing neural networks for linear programming, the proposed neural network is globally convergent to exact optimal solutions in finite time, which is remarkable and rare in the literature of neural networks for optimization. Some numerical examples are given to show the effectiveness and excellent performance of the new recurrent neural network.

This paper considers a second-order consensus problem for multiagent systems with nonlinear dynamics and directed topologies where each agent is governed by both position and velocity consensus terms with a time-varying asymptotic velocity. To describe the system's ability for reaching consensus, a new concept about the generalized algebraic connectivity is defined for strongly connected networks and then extended to the strongly connected components of the directed network containing a spanning tree. Some sufficient conditions are derived for reaching second-order consensus in multiagent systems with nonlinear dynamics based on algebraic graph theory, matrix theory, and Lyapunov control approach. Finally, simulation examples are given to verify the theoretical analysis.

Inspired by the concept of DNA sequence in biological systems, we developed a novel learning algorithm named DNA-like learning, which is enable to quickly train the CNN template (or named CNN gene) implementing linearly separable Boolean function (LSBF). This algorithm has many advantages including in particular faster running speed and better robustness, and without the need to consider its convergence property. For example, the “AND” and “OR” operations only needs 6 iterations and computations by using the algorithm, compared to the error-correction algorithm which needs 20 operations for the same task, and for judging and implementing a 9-bit linearly separable Boolean function can be finished within only one second on a program based on the new algorithm.

Complex networks are ubiquitous in the world. Many phenomena in nature can be described by the complex networks, such as brain structures, protein-protein interaction networks, scientific citation networks, food web, social interactions, the Internet, and so on. The study of complex networks is a young and active area of scientific research inspired largely by the empirical investigations of many real-world complex networks such as computer networks and social networks. It is very necessary to briefly review the main advances in the analysis, control and applications of complex networks over the last decade.

Implementing linearly nonseparable Boolean functions (non-LSBF) has been an important and yet challenging task due to the extremely high complexity of this kind of functions and the exponentially increasing percentage of the number of non-LSBF in the entire set of Boolean functions as the number of input variables increases. In this paper, an algorithm named DNA-like learning and decomposing algorithm (DNA-like LDA) is proposed, which is capable of effectively implementing non-LSBF. The novel algorithm first trains the DNA-like offset sequence and decomposes non-LSBF into logic XOR operations of a sequence of LSBF, and then determines the weight-threshold values of the multilayer perceptron (MLP) that perform both the decompositions of LSBF and the function mapping the hidden neurons to the output neuron. The algorithm is validated by two typical examples about the problem of approximating the circular region and the well-known n-bit parity Boolean function (PBF).

Universal perceptron (UP), a generalization of Rosenblatt's perceptron, is considered in this paper, which is capable of implementing all Boolean functions (BFs). In the classification of BFs, there are: 1) linearly separable Boolean function (LSBF) class, 2) parity Boolean function (PBF) class, and 3) non-LSBF and non-PBF class. To implement these functions, UP takes different kinds of simple topological structures in which each contains at most one hidden layer along with the smallest possible number of hidden neurons. Inspired by the concept of DNA sequences in biological systems, a novel learning algorithm named DNA-like learning is developed, which is able to quickly train a network with any prescribed BF. The focus is on performing LSBF and PBF by a single-layer perceptron (SLP) with the new algorithm. Two criteria for LSBF and PBF are proposed, respectively, and a new measure for a BF, named nonlinearly separable degree (NLSD), is introduced. In the sense of this measure, the PBF is the most complex one. The new algorithm has many advantages including, in particular, fast running speed, good robustness, and no need of considering the convergence property. For example, the number of iterations and computations in implementing the basic$2$-bit logic operations such asand,or, andxorby using the new algorithm is far smaller than the ones needed by using other existing algorithms such as error-correction (EC) and backpropagation (BP) algorithms. Moreover, the synaptic weights and threshold values derived from UP can be directly used in designing of the template of cellular neural networks (CNNs), which has been considered as a new spatial–temporal sensory computing paradigm.

In the literature, it was reported that the chaotic artificial neural network model with sinusoidal activation functions possesses a large memory capacity as well as a remarkable ability of retrieving the stored patterns, better than the conventional chaotic model with only monotonic activation functions such as sigmoidal functions. This paper, from the viewpoint of the anti-integrable limit, elucidates the mechanism inducing the superiority of the model with periodic activation functions that includes sinusoidal functions. Particularly, by virtue of the anti-integrable limit technique, this paper shows that any finite-dimensional neural network model with periodic activation functions and properly selected parameters has much more abundant chaotic dynamics that truly determine the model's memory capacity and pattern-retrieval ability. To some extent, this paper mathematically and numerically demonstrates that an appropriate choice of the activation functions and control scheme can lead to a large memory capacity and better pattern-retrieval ability of the artificial neural network models.

This paper introduces a novel complex network model to evaluate the reputation of virtual organizations. By using the Lyapunov function and linear matrix inequality approaches, the local synchronization of the proposed model is further investigated. Here, the local synchronization is defined by the inner synchronization within a group which does not mean the synchronization between different groups. Moreover, several sufficient conditions are derived to ensure the local synchronization of the proposed network model. Finally, several representative examples are given to show the effectiveness of the proposed methods and theories.

In this paper, a new filtering problem for sensor networks is investigated. A new type of distributed consensus filters is designed, where each sensor can communicate with the neighboring sensors, and filtering can be performed in a distributed way. In the pinning control approach, only a small fraction of sensors need to measure the target information, with which the whole network can be controlled. Furthermore, pinning observers are designed in the case that the sensor can only observe partial target information. Simulation results are given to verify the designed distributed consensus filters.

Recently four chaos-based image encryption schemes were proposed. Essentially, the four schemes can be classified into one, which is composed of two basic parts: permutation of positions and diffusion of pixel values with the same cipher-text feedback function. The operations involved in the two basic parts are determined by a pseudo random number sequence (PRNS) generated from iterating a chaotic dynamic system. According to the security requirement, the two basic parts are performed alternatively for some rounds. Despite the claim that the schemes are of high quality, we found the following security problems: 1) the schemes are not sensitive to the changes of plain-images; 2) the schemes are not sensitive to the changes of the key streams generated by any secret key; 3) there exists a serious flaw of the diffusion function; 4) the schemes can be broken with no more than [logL(MN)] + 3 chosen-images when only one iteration is used, where MN is the size of the plain- image and L is the number of different pixel values. Moreover, we found that the cryptanalysis on one of these schemes proposed by another research group is quite questionable.

Over the last decade, complex networks have been intensively studied across many fields, especially in Internet technology, biological engineering, and nonlinear science. This paper will briefly review the main advances in the investigation of complex networks, with emphasis on the recent progress of complex networks in control and synchronization.

This paper proposes a novel multiscroll chaotic system, which is different from Chua’s circuit and all its variants in most aspects of the algebraic form, circuit design, and geometrical structure of the attractor. In particular, the multiscroll attractor of this new system is more complex than that of the generalized Chua’s circuit when they both have the same number of scrolls. The dynamical behaviors of the new system are then analyzed, including the bifurcation diagram and the Lyapunov exponent spectra. Moreover, a module-based circuit diagram is designed for realizing various multiscroll attractors. Finally, experimental circuits are implemented with physical observations reported.

Based on the sawtooth wave function, this paper initiates an approach for generating novel multi-wing butterfly chaotic attractors from the generalized first and second types of modified Lorenz systems. Our theoretical analysis shows that every index-2 saddle-focus equilibrium corresponds to a unique wing in the butterfly attractors. Compared with the traditional ring-shaped multiscroll Lorenz chaotic attractors, the proposed multi-wing butterfly chaotic attractors are much easier to be constructed and implemented by analog circuits. Furthermore, a module-based unified circuit diagram is designed for realizing various multi-wing attractors.

Recently, a new image scrambling (i.e., encryption) scheme without bandwidth expansion was proposed based on two-dimensional discrete prolate spheroidal sequences. A comprehensive cryptanalysis is given here on this image scrambling scheme, showing that it is not sufficiently secure against various cryptographical attacks including ciphertext-only attack, known/chosen-plaintext attack, and chosen-ciphertext attack. Detailed cryptanalytic results suggest that the image scrambling scheme can only be used to realize perceptual encryption but not to provide content protection for digital images.

Based on the principle of energy coding, an energy function of a variety of electric potentials of a neural population in cerebral cortex is formulated. The energy function is used to describe the energy evolution of the neuronal population with time and the coupled relationship between neurons at the subthreshold and the suprathreshold states. The Hamiltonian motion equation with the membrane potential is obtained from the neuroelectrophysiological data contaminated by Gaussian white noise. The results of this research show that the mean membrane potential is the exact solution of the motion equation of the membrane potential developed in a previously published paper. It also shows that the Hamiltonian energy function derived in this brief is not only correct but also effective. Particularly, based on the principle of energy coding, an interesting finding is that in some subsets of neurons, firing action potentials at the suprathreshold and some others simultaneously perform activities at the subthreshold level in neural ensembles. Notably, this kind of coupling has not been found in other models of biological neural networks.

In this paper, stability and bifurcation of a general recurrent neural network with multiple time delays is considered, where all the variables of the network can be regarded as bifurcation parameters. It is found that Hopf bifurcation occurs when these parameters pass through some critical values where the conditions for local asymptotical stability of the equilibrium are not satisfied. By analyzing the characteristic equation and using the frequency domain method, the existence of Hopf bifurcation is proved. The stability of bifurcating periodic solutions is determined by the harmonic balance approach, Nyquist criterion, and graphic Hopf bifurcation theorem. Moreover, a critical condition is derived under which the stability is not guaranteed, thus a necessary and sufficient condition for ensuring the local asymptotical stability is well understood, and from which the essential dynamics of the delayed neural network are revealed. Finally, numerical results are given to verify the theoretical analysis, and some interesting phenomena are observed and reported.

In this paper, we propose and study a general array model of coupled delayed neural networks with hybrid coupling, which is composed of constant coupling, discrete-delay coupling, and distributed-delay coupling. Based on the Lyapunov functional method and Kronecker product properties, several sufficient conditions are established to ensure global exponential synchronization based on the design of the coupling matrices, the inner linking matrices, and/or some free matrices representing the relationships between the system matrices. The conditions are expressed within the framework of linear matrix inequalities, which can be easily computed by the interior-point method. In addition, a typical chaotic cellular neural network is used as the node in the array to illustrate the effectiveness and advantages of the theoretical results.

In this paper, a general structure based on Chua's circuit framework is proposed for the generation of n×m scroll attractors. Starting from a modified Chua's circuit with n-scroll attractor, n × m-scrolls can be duly generated and observed by adding a simple staircase function onto the state equations. This method is successfully applied to different n-scroll Chua's circuits with equi-distance equilibrium points, and the results are verified by both simulations and experiments.

In this paper, some existing perceptual encryption algorithms of MPEG videos are reviewed and some problems, especially security defects of two recently proposed MPEG-video perceptual encryption schemes, are pointed out. Then, a simpler and more effective design is suggested, which selectively encrypts fixed-length codewords in MPEG-video bit streams under the control of three perceptibility factors. The proposed design is actually an encryption configuration that can work with any stream cipher or block cipher. Compared with the previously-proposed schemes, the new design provides more useful features, such as strict size-preservation, on-the-fly encryption and multiple perceptibility, which make it possible to support more applications with different requirements. In addition, four different measures are suggested to provide better security against known/chosen-plaintext attacks.

The theory of power systems dynamics has been developed largely from detailed studies of the dynamics of simple system structures with emphasis on the effects of modeling details of the dynamics. In contrast, the recent study in the science of complex networks, motivated by numerous real-world examples in various areas including power systems, employs rather simple dynamics and yet places much more emphasis on network structures. It appears that the two approaches can usefully inform each other for further progress into an integrated study of very large (or massive) systems as well as very complex dynamics. This paper reviews recent progress in these areas and suggests fruitful lines of future research.

Over the last two decades, generating complex multi-scroll chaotic attractors via simple electronic circuits or simple systems has seen rapid development. This paper provides a brief overview of the subject on multi-scroll chaotic attractors generation, including some fundamental theories and design methodologies.

A systematic circuit design approach is proposed for experimental verification of hyperchaotic 2, 3, 4-scroll attractors from a generalized Matsumoto-Chua-Kobayashi (MCK) circuit. The recursive formulas for system parameters are rigorously derived for improving the hardware implementation.

Research of delayed neural networks with varying self-inhibitions, interconnection weights, and inputs is an important issue. In the real world, self-inhibitions, interconnection weights, and inputs should vary as time varies. In this letter, we discuss a large class of delayed neural networks with periodic inhibitions, interconnection weights, and inputs. We prove that if the activation functions are of Lipschitz type and some set of inequalities, for example, the set of inequalities 3.1 in theorem 1, is satisfied, the delayed system has a unique periodic solution, and any solution will converge to this periodic solution. We also prove that if either set of inequalities 3.20 in theorem 2 or 3.23 in theorem 3 is satisfied, then the system is exponentially stable globally. This class of delayed dynamical systems provides a general framework for many delayed dynamical systems. As special cases, it includes delayed Hopfield neural networks and cellular neural networks as well as distributed delayed neural networks with periodic self-inhibitions, interconnection weights, and inputs. Moreover, the entire discussion applies to delayed systems with constant self-inhibitions, interconnection weights, and inputs.

Many fuzzy control schemes used in industrial practice today are based on some simplified fuzzy reasoning methods, which are simple but at the expense of losing robustness, missing fuzzy characteristics, and having inconsistent inference. The concept of optimal fuzzy reasoning is introduced in this paper to overcome these shortcomings. The main advantage is that an integration of the optimal fuzzy reasoning with a PID control structure will generate a new type of fuzzy-PID control schemes with inherent optimal-tuning features for both local optimal performance and global tracking robustness. This new fuzzy-PID controller is then analyzed quantitatively and compared with other existing fuzzy-PID control methods. Both analytical and numerical studies clearly show the improved robustness of the new fuzzy-PID controller.

From the control theory point of view, it is reasonable to regard the TCP congestion control mechanism as a feedback control system. The TCP congestion control is complemented by the active queue management (AQM) scheme implemented in the routers, which could improve the effectiveness. Recently, an effective proportional-differential (PD) control algorithm has been proposed as a new AQM scheme for TCP congestion control. But it is still difficult to assign the parameter values of the PD-controller. This paper proposes a method for the design of an effective and stable PD-control AQM for routers in the Internet. For this purpose, a first-order plus time-delay TCP model is constructed, and a relay feedback method is employed to determine a set of stable parameter values of the model. From this set of values, and the requirements of the gain and phase margin, the specified parameter values of the PD-controller can be easily obtained by scanning the stable parameter set.

Using a simple model of saturated, synchronized and homogeneous sources of TCP Reno with drop-tail queue management and a discrete-time framework, we derive formulae for stationary as well as transient queueing behavior that shed light on the relationship between large buffers and work conservation (queue never empties). Using simulations, the relevance of the results for the case of non-synchronized sources is demonstrated. In particular, we demonstrate that a certain simple lower bound for the stationary queue length applies also to the case where the sources are non-stationary.

In this paper, we present a new approach for chaos reproduction using variable structure recurrent neural networks (VSRNN). A neural network identifier is designed, with a variable structure that will change according to its output performance as compared to the given orbits of an unknown chaotic systems. A tradeoff between identification errors and computational complexity is discussed.

In this paper, direct and indirect adaptive output-feedback fuzzy decentralized controllers for a class of uncertain large-scale nonlinear systems are developed. The proposed controllers do not need the availability of the state variables. By designing the state observer, the adaptive fuzzy systems, which are used to model the unknown functions, can be constructed using the state estimations, and a new hybrid adaptive fuzzy control methodology is proposed by combining the adaptive fuzzy systems with H infinity control and the sliding mode control techniques. Based on Lyapunov stability theorem, the stability of the closed-loop systems can be verified. Moreover, the proposed overall control schemes guarantee that all the signals involved are bounded and achieve the H infinity-tracking performance. To demonstrate the effectiveness of the proposed methods, simulation results are illustrated in this paper.

This paper describes a proportional-differential (PD) control algorithm as a new active queue management (AQM) scheme for TCP/IP congestion control. From the viewpoint of the control theory, TCP congestion control system can be regarded as a feedback regulating system. In this paper, a robust AQM called PD-controller is proposed. The design principles of PD-controller are presented in details. Its performance is extensively evaluated by simulations. The results demonstrate that the PD-controller AQM is stable and robust against traffic load fluctuations, UDP and HTTP disturbances. Its superiority over other AQMs is also demonstrated.

Fuzzy logic has been used as a means of interpreting vague, incomplete and even contradictory information into a compromised rule base in artificial intelligence such as machine decision–making. Within this context, fuzzy logic can be applied in the field of expert systems to provide additional flexibilities in constructing a working rule base: different experts’ opinions can be incorporated into the same rule base, and each opinion can be modeled in a rather vague notion of human language. As some illustrative application examples, this paper describes how fuzzy logic can be used in expert systems. More precisely, it demonstrates the following applications: (i) a healthcare diagnostic system, (ii) an autofocus camera lens system and (iii) a financial decision system. For each application, basic rules are described, the calculation method is outlined and numerical simulation is provided. These applications demonstrate the suitability and performance of fuzzy logic in expert systems.

This paper presents the design, tuning and performance analysis of a new predictive fuzzy controller structure for higher order plants with large time delays. The designed controller consists of a fuzzy proportional‐integral (PI) part and a fuzzy predictor. The fuzzy predictive PI controller combines the advantages of fuzzy control while maintaining the simplicity and robustness of a conventional PI controller. The dynamics of the prediction term are adaptive to the system’s time delay. The prediction term has two parts: a fuzzy predictor that uses the system time delay as an input for calculating the prediction horizon and an exponential term that uses the prediction horizon as its positive power. The prediction term also introduces phase lead into the system which compensates for the phase lag due to the time delay in the plant, thereby stabilizing the closed‐loop configuration. The performance of the proposed controller is compared with the responses of the conventional predictive PI controller, showing many advantages of the new design over its conventional counterpart.

A linear model of recurrent neural networks, called the Elman networks, is combined with the simple nonlinear modulo (mod) operation on its linear activated function so as to generate chaos purposely. Conditions on the weight matrix are obtained, under which the generated chaos satisfies the mathematical definition of chaos in the sense of T.Y. Li and J.A. Yorke (1975). Some simple and representative weight matrices are constructed for designing such Elman networks that can generate Li-Yorke chaos. Several numerical simulations are shown to verify and visualize the design.

Addresses the robust fuzzy control problem for nonlinear systems in the presence of parametric uncertainties. The Takagi-Sugeno (T-S) fuzzy model is adopted for fuzzy modeling of the nonlinear system. Two cases of the T-S fuzzy system with parametric uncertainties, both continuous-time and discrete-time cases are considered. In both continuous-time and discrete-time cases, sufficient conditions are derived for robust stabilization in the sense of Lyapunov asymptotic stability, for the T-S fuzzy system with parametric uncertainties. The sufficient conditions are formulated in the format of linear matrix inequalities. The T-S fuzzy model of the chaotic Lorenz system, which has complex nonlinearity, is developed as a test bed. The effectiveness of the proposed controller design methodology is finally demonstrated through numerical simulations on the chaotic Lorenz system.

A new adaptive fuzzy control algorithm is developed in this paper, which has a regular fuzzy controller and a supervisory control term. This control algorithm does not require the system model, but has stability assurance for the closed-loop controlled system. The design is simple, in the sense that both the membership functions and the rule base are simple, yet generic. It can be applied to a large class of robotic and other mechanical systems.

In this paper, a new structure of predictive fuzzy PID controller is proposed. The new controller is robust and effective in controlling higher order and time-delayed complex processes. The proposed predictive fuzzy PID controller combines the fuzzy PID and generalized predictive control (GPC) ideas together, and is equipped with optimization capability that minimizes a cost function. These features make the new controller more effective than individual fuzzy PID and GPC controllers in handling nonlinear systems. Computer simulations are shown for various types of process stabilization and set point tracking problems.

This paper investigates the complex dynamical phenomena such as bifurcations and chaos in a structure of strongly coupled neural oscillators. Bifurcation diagrams and topological properties of these periodic solutions are then obtained, where synchronization phenomena are completely classified. A new bursting response is also observed and discussed.

Anti-control of chaos, making a non-chaotic system chaotic, has led to the discovery of some new chaotic systems, particularly the continuous-time three-dimensional autonomous Chen's equation with only two quadratic terms. This paper further investigates some basic dynamical properties and various bifurcations of Chen's equation, thereby revealing its different features from some other chaotic models such as the Lorenz system.

In this paper, the problem of making a nonchaotic continuous-time system chaotic via nonlinear time-delay feedback is studied. The designed controller is a combination of a feedback stabilization law and a time-delay feedback law with an arbitrarily small-amplitude, which together can make the system chaotic. An example is included for illustration.

Existence and uniqueness of equilibrium, as well as its stability and instability, of a continuous-time Hopfield neural network are studied. A set of new and simple sufficient conditions are derived.

We develop a hybrid state-space fuzzy model-based controller with dual-rate sampling for digital control of chaotic systems. A Takagi-Sugeno (TS) fuzzy model is used to model the chaotic dynamic system and the extended parallel-distributed compensation technique is proposed and formulated for designing the fuzzy model-based controller under stability conditions. The optimal regional-pole assignment technique is also adopted in the design of the local feedback controllers for the multiple TS linear state-space models. The proposed design procedure is as follows: an equivalent fast-rate discrete-time state-space model of the continuous-time system is first constructed by using fuzzy inference systems. To obtain the continuous-time optimal state-feedback gains, the constructed discrete-time fuzzy system is then converted into a continuous-time system. The developed optimal continuous-time control law is finally converted into an equivalent slow-rate digital control law using the proposed intelligent digital redesign method. The main contribution of the paper is the development of a systematic and effective framework for fuzzy model-based controller design with dual-rate sampling for digital control of complex such as chaotic systems. The effectiveness and the feasibility of the proposed controller design method is demonstrated through numerical simulations on the chaotic Chua circuit.

A new multi-input multi-output (MIMO) fuzzy proportional-derivative (PD) controller is designed and analyzed in this paper for its asymptotic stability when used for multi-link robot arm systems. Simple sufficient conditions for designing stable control gains are derived via the Lyapunov method.

This paper provides a suboptimal solution to the problem of automatically back-driving a truck using the natural parabolic paths as the shortest moving distance requirement. By applying fuzzy logic control techniques, a controller with nine rules is developed, which works well even without using a mathematical system model. As long as the states (position and orientation) of the truck are measurable at each discrete-time step during the control process, this controller can drive the truck to follow any feasible trajectories (their smallest radii are no less than the smallest radius of the curve along which the truck can travel), and to move successfully into a prescribed parking lot. In addition to the design of the controller, controllability and stability of the control system are briefly discussed under the condition that only partial information about the current states of the system are available. Simulation results are presented, to demonstrate the accuracy and effectiveness of this new fuzzy logic controller and to compare its control performance with other fuzzy logic controllers that were designed for the same purpose under the same conditions but without using any optimality criterion.

Our interest in this paper is to design and apply the simplest possible artificial neural networks for identifying and controlling chaotic systems. To illustrate the effectiveness of these NN controllers, we show some convincing computer simulations in the identification and control of the chaotic Duffing oscillator and chaotic cellular neural networks.

This paper describes the design principle, tracking performance, and stability analysis of a fuzzy proportional-derivative (PD) controller. First, the fuzzy PD controller is derived from the conventional continuous-time linear PD controller. Then, the fuzzification, control-rule base, and defuzzification in the design of the fuzzy PD controller are discussed in detail. The resulting controller is a discrete-time fuzzy version of the conventional PD controller, which has the same linear structure in the proportional and the derivative parts but has nonconstant gains: both the proportional and derivative gains are nonlinear functions of the input signals. The new fuzzy PD controller thus preserves the simple linear structure of the conventional PD controller yet enhances its self-tuning control capability. Computer simulation results have demonstrated this advantage of the fuzzy PD controller, particularly when the process to be controlled is nonlinear. After a detailed stability analysis, where a simple and realistic sufficient condition for the bounded-input/bounded-output stability of the overall feedback control system was derived, several computer simulation results are compared with the conventional PD controller. Although the conventional and fuzzy PD controllers are not exactly comparable, the authors compare them in order to have a sense of how well the fuzzy PD controller performs. For this reason, in the simulations several first-order and second-order linear systems, with or without time-delays, are first used to test the performance of the fuzzy PD controller for step reference inputs: the fuzzy PD control systems show remarkable performance, as well as (if not better than) the conventional PD control systems. Moreover, the fuzzy PD controller is compared to the conventional PD controller for a particular second-order linear system, showing the advantage of the fuzzy PD controller over the conventional one in the sense that in order to obtain the same control performance the conventional PD controller has to employ an extremely large gain while the fuzzy controller uses a reasonably small gain. Finally, in the case of nonlinear systems, the authors provide some examples to show that the fuzzy PD controller can track the set-points satisfactorily but the conventional PD controller cannot.>

The unified approach to optimal image interpolation problems presented provides a constructive procedure for finding explicit and closed-form optimal solutions to image interpolation problems when the type of interpolation can be either spatial or temporal-spatial. The unknown image is reconstructed from a finite set of sampled data in such a way that a mean-square error is minimized by first expressing the solution in terms of the reproducing kernel of a related Hilbert space, and then constructing this kernel using the fundamental solution of an induced linear partial differential equation, or the Green's function of the corresponding self-adjoint operator. It is proved that in most cases, closed-form fundamental solutions (or Green's functions) for the corresponding linear partial differential operators can be found in the general image reconstruction problem described by a first- or second-order linear partial differential operator. An efficient method for obtaining the corresponding closed-form fundamental solutions (or Green's functions) of the operators is presented. A computer simulation demonstrates the reconstruction procedure.

A suboptimal trajectory planning problem for single-link flexible-joint robot arms is studied. A global feedback-linearization technique is first applied to reformulate the nonlinear constrained optimization as a suboptimal interpolation problem. Then the unique analytic suboptimal solution for the problem is obtained in closed form. Simulation results are given to show the effectiveness of the method.>

Consideration is given to an optimal modeling problem for the general horizontally stratified ocean, which is assumed to be a random inhomogeneous medium. The random acoustic wave velocity potential p=p(x, y, z) in the ocean is described by the stochastic Helmholtz equation Delta p+k/sup 2/p=0, where Delta is the standard Laplacian partial differential operator, and k=k(x, y, z) is the random wave number. Because of the random and inhomogeneous nature of the ocean, not only the amplitude and phase fluctuations of the sound wave but also its scattering have to be taken into account in the mathematical modeling of the random wave propagation. In this consideration, p is decomposed as p=p/sub 0/+p/sub s/, where p/sub 0/ is the deterministic component (the unperturbed part) of the velocity potential (which can be determined by some existing techniques) and p/sub s/ is the random component created essentially by a perturbation. A novel method for obtaining an optimal estimate of p/sub s/ is proposed. It is based on a PDL/sub g/-spline theory and technique developed by the authors, so that p can be determined optimally and efficiently for the purpose of applications.>

The problem of model-based optimal reconstruction of an image from its samples is studied. It is assumed that the image signal is described by a linear PDE (partial differential equation) model from which a sequence of output frames is available. These frames need not have rectangular boundaries or be uniformly sampled. Under the criterion that the image to be reconstructed is the one that is created by an unknown input signal with minimum energy, the authors obtain a unique optimal solution by interpolating the image samples with a recently formulated generalized spline called the PDL/sub g/ spline. It is possible to show that such a reconstruction corresponds to a minimum-mean-squares estimate of the image, given its samples. The authors also derive an algorithm for finding the optimal solution in an explicit and closed form. They include some computer simulation results to show the quality of the images obtained with the method.>