This paper investigates the problem of eco-friendly autonomous driving platoon control with integrated privacy preserving. A unified car-follower modeling framework is proposed to address single-lane, multi-lane, and mode transition platoon merging scenarios. To safeguard information privacy while maintaining control accuracy, the stochastic vector obfuscation mechanism is developed. Corresponding privacy-preserving control strategies and privacy multiplication protocols (PMP) are designed for each scenario. Theoretical analyses establish stability, consensus, and privacy guarantees. Numerical simulations further confirm the effectiveness in preserving privacy and stability. Moreover, comparative experiments show that the proposed approach outperforms existing methods in terms of privacy preservation, real-time performance, and control accuracy.

The intelligent connected transportation system represents an inevitable trend, reshaping both traffic participants and control mechanisms. As the number of connected and autonomous vehicles increases, traffic flow is transitioning to a mixed environment of autonomous and manually driven vehicles. The transition to mixed traffic flows introduces critical privacy risks, notably real-time location tracking and unauthorized data collection. To address these challenges, we propose a privacy-aware micro-behavior coordination framework. It combines secure computation protocols and fine-grained control mechanisms for car-following and lane-changing behaviors. In this way, the approach simultaneously maintains traffic efficiency and data privacy. Theoretical proofs and numerical simulations demonstrate the effectiveness of the framework in safeguarding sensitive information while maintaining smooth traffic flow. Critically, our solution bridges the gap between collaborative driving and privacy preservation in mixed traffic.

The consensus control protocol of the cooperative-competitive network requires nodes to transmit their own information to the rival group, which is detrimental to the security of the information. In this paper, we propose a novel node decomposition mechanism, which can prevent the state information from being revealed during the information exchange for multi-agent systems with antagonistic interactions. For each node, one of the two subnodes takes over the role of the primitive node with cooperative neighbors, and the other one is involved in antagonistic interactions. Under this method, the connectivity and structurally balanced of the system are not changed, so it can still achieve bipartite consensus. Besides, although the initial values of the two subnodes are chosen randomly, the average of these subnodes corresponds to the original state value, ensuring precise bipartite consensus. Moreover, we also prove that the privacy of a node can be guaranteed if and only if it has a neighbor in the same group. The effectiveness of the proposed approach is demonstrated by a numerical example.

This paper investigates the problem of fixed-time stability of nonlinear systems subject to destabilizing delayed impulses. The existing literature usually uses inequality-based techniques to deal with impulses and delays, which leads to considerable conservatism, especially when systems contain large impulsive gains or large delays. In contrast, inspired by the Möbius transformation, this article presents necessary and sufficient criteria for fixed-time stability of nonlinear systems subject to periodic destabilizing impulses with delay, or even with arbitrarily finite delays. To conquer the challenge caused by large delays, this article proposes a generic framework that equivalently transforms a system with large delayed impulses into a series of systems with small delayed impulses. The equivalence of this transformation does not induce any conservatism. The criteria reveal that as the delay increases, the system switches between stability and instability. In addition, it proved that the impulsive systems under some conditions exhibit a subcritical Hopf bifurcation: If the impulsive frequency is less than a critical value, then the system converges globally to an equilibrium point in a fixed time; otherwise the system oscillates periodically. Finally, examples of circuit systems are used to validate the theoretical results.

For high-dimensional heterogeneous Kuramoto oscillator networks (HDHKONs) evolving in continuous time, achieving global synchronization can be exceedingly challenging, and in many cases, it may even appear impossible for various network configurations, including Platonic solids and Archimedean solids, or large-scale networks. Herein, a pinning impulsive control approach for HDHKONs is developed to attain global synchronization on the unit sphere without imposing constraints on initial phase distributions. With this approach, the entire network is globally stabilized onto an objective trajectory by impulsively controlling only a small fraction of oscillators. Furthermore, several synchronization criteria are provided to ensure that the global synchronization procedure is successful. These criteria are easily verified and shed light on the interplay among network parameters, the percentage of controlled oscillators, impulsive intensity, and impulsive frequency. Finally, two examples are implemented to validate the theoretical results.

This article provides a new impulsive observation approach [called impulsive adaptive observer, impulsive adaptive observation (IAO)] for a class of linear systems. A discrete-time-based adaptive rule for the impulsive observer gain is designed using only output information at discrete-time intervals (or impulsive instants), overcoming the real-time data requirement of continuous-time adaptive observation frameworks. The IAO effectively estimates the states of a continuous-time system and demonstrates outstanding state tracking performance in practical implementations. Furthermore, the IAO-based feedback controller is designed to stabilize the controlled plant. Stability criteria for the IAO protocols are established, showing improved performance over existing schemes by reducing computational load and enhancing control flexibility. The simulations for the electrical system are presented finally to confirm the effectiveness of the IAO and its control approach.

This paper addresses the leader-following consensus problems in nonlinear multi-agent systems (MASs), focusing on handling malicious denial-of-service (DoS) attacks. Initially, we introduce an innovative dynamic event-triggered scheme to mitigate network congestion induced by DoS attacks. This scheme, utilizing sampled data, aims to minimize the harmful effects of attacks, and ensures the proficient allocation of limited network resources. Specifically, the sampling period automatically switches depending on the system’s attack status, while the threshold parameter within the predefined triggering condition can be adaptively tuned to match the dynamic characteristics of the controlled system. Building upon this, we propose an event-driven control protocol, along with the construction of a new switched MASs model. It is shown, both analytically and numerically, that our designed control strategy exhibits superiority over traditional co-design frameworks from the aspect of three pivotal metrics: average number of event triggers (ANET), convergence time, and control cost.

The storage and transmission of large-scale data are recognized as significant challenges that incur substantial costs due to the massive volume of information involved. Lossless compression offers a potential solution to this problem. In this work, we explore the online lossless state compression (LSC) in finite-valued networks by effectively combining the methods of finite state automata and reinforcement learning. To achieve online lossless compression, the concept ofk-step compressed walks (state sequences) is introduced. By constructing a finite state automaton to identify all insertable walks, the recoverability conditions of online lossless compression are presented. For any given compressed walkw’c, one algorithm is proposed to find a minimal recoverablekmin-step compressed walk, thereby improving the compression ratio. Furthermore, it can be found that if a compressed walk keeps recoverability, adding more states to it would not break this property. Additionally, a model-free reinforcement learning framework based on Q-learning is developed to obtain globally minimal recoverable compressed walks. Finally, a numerical example is given to demonstrate the efficiency of the proposed online lossless compression scheme, achieving a compression ratio of 44.4%.

In intelligent transportation systems (ITS), machine learning is highly effective in anomaly detection for state estimation (SE) in traffic flow measurement, but it requires resource-intensive collection of anomaly samples and overlooks spatial characteristics. Additionally, the original SE in traffic flow measurement exhibits low-frequency characteristics due to computational complexity. Considering these limitations, this paper proposes a fast and efficient anomaly detection framework for SE in traffic flow measurement. Initially, an attention-based spatiotemporal graph convolutional network (ASTGCN) model is utilized to extract both temporal and spatial features of SE. The ASTGCN model is trained using quantile regression, relying solely on normal samples during training. This approach eliminates the need for collecting anomalous samples and reduces computational demands. The model establishes a safe interval for SE that significantly improves anomaly detection capabilities. Furthermore, a teacher-student network is implemented, where the teacher network, trained offline, distills its ability to convert low-frequency SE data into high-frequency representations into a simpler student network. The student network executes real-time reconstruction of high-frequency SE, thus enhancing the precision of anomaly detection without substantial resource expenditure. Finally, the analysis conducted on the California’s 7th district highway measurement system demonstrates the proposed method’s ability to accurately detect anomalous SE in traffic flow measurement.

In this article, we propose a new concept called average impulsive delay-gain (AIDG) for studying the synchronization of coupled neural networks (CNNs). Based on the viewpoints of impulsive control and impulsive perturbation, we establish some globally exponential synchronization criteria for CNNs. Our methods are well-suited for addressing the synchronization problems of systems subject to hybrid delayed impulses with time-varying impulsive delay and gain. Moreover, we prove that the AIDG has both positive and negative effects on synchronization. Compared to existing research, our conclusions are more applicable and less conservative as the considered hybrid delayed impulses involve more flexible cases. Finally, we validate the effectiveness of our proposed results by applying them to small-world and scale-free network models.

This article develops a novel event-triggered finite-time control strategy to investigate the finite-time synchronization (F-tS) of fractional-order memristive neural networks with state-based switching fuzzy terms. A key distinction of this approach, compared with existing event-based finite-time control schemes, is the linearity of the measurement error function in the event-triggering mechanism (ETM). The advantage of linear measurement error not only simplifies computational tasks but also aids in demonstrating the exclusion of Zeno behavior for fractional-order systems (FSs). Furthermore, to derive F-tS criteria in the form of linear matrix inequalities (LMIs), a novel finite-time analytical framework for FSs is proposed. This framework includes two original inequalities and a weighted-norm-based Lyapunov function. The effectiveness and superiority of the theoretical results are demonstrated through two examples. Both theoretical and experimental results suggest that the criteria obtained using the new analytical framework are less conservative than existing results.

In this article, set stabilization in switched Boolean networks is investigated through link augmentations. Link augmentation is introduced as a selective process for adding specific edges between nodes in the wiring digraph of the network. For the implementation of link augmentation, various variables are integrated into the dynamics governing networks, utilizing basic logical operators. A key aspect of this article is the incorporation of additional functions introduced by the link augmentations into the original dynamics of the system using constrained logical operators. Further, several criteria for set stabilization are formulated, and the link augmentation control strategy is innovatively designed, utilizing theQ-learning Algorithm. Finally, a biological example is presented to demonstrate the effectiveness of the proposed methods.

This article studies a more realistic issue in multiagent systems (MASs) named open topology, where the network scale tends to be variable as agents may join, leave, or be replaced. In order to reveal the influence that the variation of network scale brings on the dynamic behavior of MASs, a novel transition process containing impulse is provided. Then by applying the Halanay-like inequality, the distributed sampled-data control is designed to ensure the consensus property of the MASs under open topology. It is shown that the derived results can degenerate into the consensus criteria for general MASs with fixed-scale topology. Also, the potential packet loss phenomenon existing in controller is considered, which is integrated into the consensus performance via the average packet loss interval (APLI) condition, thereby guaranteeing the robustness of consensus performance against packet loss. Moreover, within the framework of open topology, it is proved that the admissible packet loss for MASs can be estimated in an average sense. At the end, the availability of this article is demonstrated by discussing a numerical example.

Optimal energy management of a power system enables the economic operation of grids. However, traditional centralized methodologies face limitations when dealing with large-scale power systems. To overcome these challenges, an optimal energy management model is developed for networked microgrids (NMGs), and a distributed neurodynamic optimization algorithm is proposed for the optimization model. Before facilitating power exchange between neighboring microgrids (MGs), a strict priority scheme for power distribution is outlined. Distributed power generation takes precedence in meeting load requirements, followed by charging and discharging operations. Furthermore, to ensure the stability of the overall grid, power transmission is established between neighboring MGs. To solve the optimization problem, a distributed recurrent neural network is developed, and it is demonstrated to converge towards an optimal solution. An illustrative example involving 3-MG NMGs is elaborated to demonstrate the validity and effectiveness of the proposed algorithm.

The development of integrated energy system has promoted the development of the power system into the largest and most complex cyber-physical energy system, where the change in the openness of the load frequency control (LFC) system has also increased its susceptibility to false data injection attacks (FDIAs). This paper porposes an artificial intelligence (AI) based detection and countermeasure strategy to protect LFC systems from FDIAs. First, The levenberg-marquarelt-back propagation (LM-BP) neural networks (NNs) is trained by collecting the historical data of frequency deviation, power deviation of contact line, and active power load deviation. Second, the output control signal of LM-BP NNs is tested against the output of the system controller for residuals to determine whether has FDIAs. Furthermore, to resist the negative effects of FDIAs, the control signal calculated by the LM-BP NNs will replace the traditional proportion integration differentiation (PID) output. Finally, The advantages of the proposed strategy are illustrated by the two interconnected power systems.

In this article, we are devoted to addressing the state-feedback set stabilization of Boolean control networks with state-dependent random impulses by utilizing a hybrid index model. By comparison with the previous impulsive Boolean networks, this model can be used to describe the instantaneousness of various impulsive behaviors more clearly. In order to avoid the occurrence of Zeno phenomenon, we first introduce the basic concept of forward completeness and further establish the judging criterion. After that, an algorithm is presented to derive the largest control invariant subset of a given subset. Based on this, we derive a necessary and sufficient criterion for finite-time feedback set stabilizability. Similarly, the result is also obtained for the asymptotic case, and the asymptotic set stabilizers are designed by dividing the whole state space into several layers. Moreover, we also investigate the relationships between different stabilizabilities. Last, two illustrative examples are presented to demonstrate the efficiency of the theoretical results.

In gene regulatory networks (GRNs), it is important to model gene regulation based on a priori information and experimental data. As a useful mathematical model, probabilistic Boolean networks (PBNs) have been widely applied in GRNs. This article addresses the optimal reconstruction problem of PBNs based on several priori Boolean functions and sampled data. When all candidate Boolean functions are known in advance, the optimal reconstruction problem is reformulated into an optimization problem. This problem can be well solved by a recurrent neural network approach which decreases the computational cost. When parts of candidate Boolean functions are known in advance, necessary and sufficient conditions are provided for the reconstruction of PBNs. In this case, two types of reconstruction problems are further proposed: one is aimed at minimizing the number of reconstructed Boolean functions, and the other one is aimed at maximizing the selection probability of the main dynamics under noises. At last, examples in GRNs are elaborated to demonstrate the effectiveness of the main results.

This article focuses on the stability issue of switched network control systems (SNCSs) under deception attacks described by a Bernoulli process with unknown probability distribution. The false information in deception attacks is unknown but bounded and may be state dependent or state independent. By means of the input-to-state stability (ISS) tool and the convex combination method, an improved lemma is first developed for SNCSs, which facilitates the derivations of our results. After that, some attack-independent sufficient conditions for the ISS of SNCSs are obtained for mode-dependent average dwell time switching and stochastic switching, respectively. Different from existing results, the concerned switching contributes to the stability of SNCSs, which benefits the ISS performance of SNCSs even though the unknown deception attacks cause all subsystems to be non-ISS. The proposed results provide an effective solution with strong robustness to deal with unknown deception attacks or denial-of-service attacks.

Vehicle intelligent terminals often require end-user applications (APPs) to continuously send information to external data aggregator for monitoring or control tasks. However, communication channels exposed to the open environment can lead to an undesirable loss of privacy for drivers, despite the benefits provided by these APPs. It is worth mentioning that different APPs of vehicle intelligent terminals may require different key information. Given these personalized application scenarios, the use of traditional privacy protection technology may encounter limitations. To address this problem, we propose a compressive privacy-preserving algorithm that employs a compression matrix to maintain the normal function of applications while ensuring privacy. Specifically, the algorithm utilizes sensors to linearly transform the original vectors of measurements at each time step into a lower-dimensional space. The compressed measurements are then transmitted to a fusion center. Optimization problems are formulated for the current time step as well as two time steps. The performance of the algorithm is evaluated using the Cramer-Rao bound. Simulation results and comparisons further validate the effectiveness of the compressive privacy algorithm.

In real networks, communication constraints often prevent the full exchange of information between nodes, which is inevitable. This brief investigates the problem of time delay and randomly missing data in Boolean networks (BNs). A Bernoulli random variable is assigned to each node to characterize the probability of data packet dropout. Time delay and missing data are modeled by independent random variables. A novel data-sending rule that incorporates both communication constraints is proposed. An augmented system, comprising current states, delayed information, and successfully transmitted data, is established for theoretical analysis. Using the semitensor product (STP), the necessary and sufficient condition for asymptotic stability of delayed BNs with random data dropouts is derived. The convergence rate is also obtained.

This article is concerned with the event-triggered synchronization of Lur'e systems subject to actuator saturation. Aiming at reducing control costs, a switching-memory-based event-trigger (SMBET) scheme, which allows a switching between the sleeping interval and the memory-based event-trigger (MBET) interval, is first presented. In consideration of the characteristics of SMBET, a piecewise-defined but continuous looped-functional is newly constructed, under which the requirement of positive definiteness and symmetry on some Lyapunov matrices is dropped within the sleeping interval. Then, a hybrid Lyapunov method (HLM), which bridges the gap between the continuous-time Lyapunov theory (CTLT) and the discrete-time Lyapunov theory (DTLT), is used to make the local stability analysis of the closed-loop system. Meanwhile, using a combination of inequality estimation techniques and the generalized sector condition, two sufficient local synchronization criteria and a codesign algorithm for the controller gain and triggering matrix are developed. Furthermore, two optimization strategies are, respectively, put forward to enlarge the estimated domain of attraction (DoA) and the allowable upper bound of sleeping intervals on the premise of ensuring local synchronization. Finally, a three-neuron neural network and the classical Chua's circuit are used to carry out some comparison analyses and to display the advantages of the designed SMBET strategy and the constructed HLM, respectively. Also, an application to image encryption is provided to substantiate the feasibility of the obtained local synchronization results.

This brief studies the distributed synchronization of time-delay coupled neural networks (NNs) with impulsive pinning control involving stabilizing delays. A novel differential inequality is proposed, where the state's past information at impulsive time is effectively extracted and used to handle the synchronization of coupled NNs. Based on this inequality, the restriction that the size of impulsive delay is always limited by the system delay is removed, and the upper bound on the impulsive delay is relaxed, which is improved the existing related results. By using the methods of average impulsive interval (AII) and impulsive delay, some relaxed criteria for distributed synchronization of time-delay coupled NNs are obtained. The proposed synchronization conditions do not impose on the upper bound of two consecutive impulsive signals, and the lower bound is more flexible. Moreover, our results reveal that the impulsive delays may contribute to the synchronization of time-delay systems. Finally, typical networks are presented to illustrate the advantage of our delayed impulsive control method.

In this paper, an efficient image encryption scheme based on a novel mixed linear–nonlinear coupled map lattice (NMLNCML) system and DNA operations is presented. The proposed NMLNCML system strengthens the chaotic characteristics of the system, and is applicable for image encryption. The main advantages of the proposed method are embodied in its extensive key space; high sensitivity to secret keys; great resistance to chosen-plaintext attack, statistical attack, and differential attack; and good robustness to noise and data loss. Our image cryptosystem adopts the architecture of scrambling, compression, and diffusion. First, a plain image is transformed to a sparsity coefficient matrix by discrete wavelet transform, and plaintext-related Arnold scrambling is performed on the coefficient matrix. Then, semi-tensor product (STP) compressive sensing is employed to compress and encrypt the coefficient matrix. Finally, the compressed coefficient matrix is diffused by DNA random encoding, DNA addition, and bit XOR operation. The NMLNCML system is applied to generate chaotic elements in the STP measurement matrix of compressive sensing and the pseudo-random sequence in DNA operations. An SHA-384 function is used to produce plaintext secret keys and thus makes the proposed encryption algorithm highly sensitive to the original image. Simulation results and performance analyses verify the security and effectiveness of our scheme.

This paper first investigates the synchronization design problem for both Boolean networks (BNs) and singular BNs. According to the complete family of reachable sets, all possible synchronized response BNs and all possible weakly synchronized response singular BNs can be constructed. Subsequently, it is noted that there is similarity between synchronized response (singular) BNs and state observers. The synchronized response (singular) BN is constructed based on the state of a given drive (singular) BN, making its state gradually tend to be consistent with the state of the given drive (singular) BN. While the state observer is designed based on the output of a given real (singular) BN, making its state (state estimation) gradually tend to be consistent with the state of the given real (singular) BN. Therefore, consider applying the results for constructing synchronized response (singular) BNs to designing state observers for (singular) BNs. Specifically, the real (singular) BN to be observed can be regarded as a drive (singular) BN. Consequently, the problem for designing state observers can be transformed into the problem for constructing response (singular) BNs that achieve synchronization with a given real (singular) BN, and then the gain matrix of the designed state observer can be obtained by solving a matrix equation. The method for designing state observers is superior to other methods in that the accurate estimated time for designed state observers can be determined and adjusted to some certain extent, and all possible state observers in the considered form can be designed.

This article investigates the synchronization of communication-constrained complex dynamic networks subject to malicious attacks. An observer-based controller is designed by virtue of the bounded encode sequence derived from an improved coding-decoding communication protocol. Moreover, taking the security of data transmission into consideration, the denial-of-service attacks with the frequency and duration characterized by the average dwell-time constraint are introduced into data communication, and their influence on the coder string is analyzed explicitly. Thereafter, by imposing reasonable restrictions on the transmission protocol and the occurrence of attacks, the boundedness of coding intervals can be obtained. Since the precision of data is generally limited, it may lead to the situation that the signal to be encoded overflows the coding interval such that it results in the unavailability of the developed coding scheme. To cope with this problem, a dynamic variable is introduced to the design of the protocol. Subsequently, based on the Lyapunov stability theory, sufficient conditions for ensuring the input-to-state stability of the synchronization error systems under the communication-constrained condition and malicious attacks are presented. The validity of the developed method is finally verified by a simulation example of chaotic networks.

The dynamical study of continuous-/discontinuous-time fractional-order neural networks (FONNs) has been thoroughly explored, and several publications have been made available. This study is designed to give an exhaustive review of the dynamical studies of multidimensional FONNs in continuous/discontinuous time, including Hopfield NNs (HNNs), Cohen-Grossberg NNs, and bidirectional associative memory NNs, and similar models are considered in real ( [Formula: see text]), complex ( [Formula: see text]), quaternion ( [Formula: see text]), and octonion ( [Formula: see text]) fields. Since, in practice, delays are unavoidable, theoretical findings from multidimensional FONNs with various types of delays are thoroughly evaluated. Some required and adequate stability and synchronization requirements are also mentioned for fractional-order NNs without delays.

This article is dedicated to investigating the impulsive-based almost surely synchronization issue of neural network systems (NSSs) with quality-of-service constraints. First, the communication network considered suffers from random double deception attacks, which are modeled as a nonlinear function and a desynchronizing impulse sequence, respectively. Meanwhile, the impulsive instants and impulsive gains are randomly and only their expectations are available. Second, by taking two different types of random deception attacks into consideration, a novel mathematical model for vulnerable NSSs is constructed. Then, almost surely synchronization criteria are established by using Borel-Cantelli lemma. Furthermore, based on the derived strong and weak sufficient conditions, the almost surely synchronization of NSSs is achieved. Finally, the section of numerical example is shown to illustrate the effectiveness of the proposed method.

Data loss is often random and unavoidable in realistic networks due to transmission failure or node faults. When it comes to Boolean control networks (BCNs), the model actually becomes a delayed system with unbounded time delays. It is difficult to find a suitable way to model it and transform it into a familiar form, so there have been no available results so far. In this article, the stabilization of BCNs is studied with Bernoulli-distributed missing data. First, an augmented probabilistic BCN (PBCN) is constructed to estimate the appearance of data loss items in the model form. Based on this model, some necessary and sufficient conditions are proposed based on the construction of reachable matrices and one-step state transition probability matrices. Moreover, algorithms are proposed to complete the state feedback stabilizability analysis. In addition, a constructive method is developed to design all feasible state feedback controllers. Finally, illustrative examples are given to show the effectiveness of the proposed results.

In this article, minimal pinning control for oscillatority (i.e., instability) of Boolean networks (BNs) under algebraic state space representations method is studied. First, two criteria for oscillatority of BNs are obtained from the aspects of state transition matrix (STM) and network structure (NS) of BNs, respectively. A distributed pinning control (DPC) from these two aspects is proposed: one is called STM-based DPC and the other one is called NS-based DPC, both of which are only dependent on local in-neighbors. As for STM-based DPC, one arbitrary node can be chosen to be controlled, based on certain solvability of several equations, meanwhile a hybrid pinning control (HPC) combining DPC and conventional pinning control (CPC) is also proposed. In addition, as for NS-based DPC, pinning control nodes (PCNs) can be found using the information of NS, which efficiently reduces the high computational complexity. The proposed STM-based DPC and NS-based DPC in this article are shown to be simple and concise, which provide a new direction to dramatically reduce control costs and computational complexity. Finally, gene networks are simulated to discuss the effectiveness of theoretical results.

This article investigates the privacy-preserving average consensus problem in multiagent systems. A new approach is proposed to achieve the accurate average consensus value while protecting the initial state information of agents. The key idea to achieve these goals is based on partial information transmission. Each agent decomposes its initial state information into several different subinformation. The values of these subinformation are chosen randomly but with their mean value fixed to the original initial value. Then, based on multiple communication channels, agents share all their subinformation, but ensure that each neighbor can only obtain partial subinformation. We prove that the privacy can be protected under our method if each agent has at least two neighbors, and one of the neighbors is neutral. The generalization on the directed graph about this method is also considered. Finally, two examples are provided to illustrate the design process and practical applications of the proposed approach.

In this study, we discuss how multi-agent systems (MASs) with a leader can achieve distributed bipartite tracking consensus using asynchronous impulsive control strategies. The proposed asynchronous impulsive control approach does not require the impulse to occur simultaneously for all agents. The communication links between neighboring nodes of MASs are antagonistic. When the leader’s control input is non-zero, sufficient conditions are obtained to achieve bipartite asynchronous impulsive tracking consensus in closed-loop MASs. More extensive ranges of asynchronous impulsive effects are discussed, and the designed controller’s feedback can effectively work against adverse impulsive permutation. Simple algebraic conditions for estimating the impulsive gain boundary and asynchronous impulsive interval are presented. Theoretical results are demonstrated with illustrative examples.

In this paper, a novel constrained switching rule, called “time-triggered logical switching” (TTLS) is considered for switched logical dynamic systems (SLDSs). Compared with the general time-triggered switching, the activation mode of TTLS cannot be arbitrary and is pre-allocated according to the logic operation, which is more practical. The TTLS is described as an LDS, and according to the characteristics of LDS, the stability analysis of SLDSs with TTLS is converted into the stability analysis of SLDSs under the logical switching cycle sequences. Firstly, based on the equivalent algebraic form of SLDSs with TTLS, combining the Lyapunov theory of LDS with average dwell-time method, several sufficient conditions are put forward for ensuring the point stability of the considered SLDSs. Then, by defining the switching cycle invariant subset and constructing a new system, the set stability analysis of the original system is transformed into the point stability analysis of the new system, and further, the obtained results for the point stability analysis are applied to the set stability analysis. At last, the validity of obtained results is illustrated by simulation on gene and protein signaling activity patterns.

This paper focuses on the synchronization control issue of networked systems. Due to the imperfect network environment, continuous or precise transmission is impractical, and intermittent communication scheme under state quantization needs to be considered. First, an easy-to-implement dynamic quantizer, which possesses finite quantization level, is designed to deal with the imprecise information sharing. Next, based on the designed quantizer, a dynamic estimator is introduced to estimate the real-time state information and generate control inputs. An event-based communication scheme is utilized to ensure that the estimate error does not exceed a certain threshold. Then, detailed design of the dynamically quantized controller is given to achieve exact synchronization, and corresponding distributed design is also provided to improve the feasibility. Moreover, some results for practical synchronization are derived. Finally, the validity of our theoretical results is illustrated by two numerical examples.

Demand response (DR) of power grids services an increasing key component of smart grids. This article is devoted to the DR active power control for smart buildings based on a cloud platform for security interconnection with power grids. The objective of the DR control is to cope with the intermittent renewable power injection and power fluctuation of the tie-line between the building and the distribution grid. The renewable energy power includes photovoltaic panel and on-site wind power generators on the building roof, and the flexible loads includes electric vehicles (EVs) connected to the building, and thermostatically controlled loads (TCLs) in the building. We propose two fair and flexible indexes, comfortable levels for TCLs and the charging priority for EVs, and design two kinds of DR control algorithm, i.e., centralized load reduction control algorithm and distributed load following control algorithm, to coordinate the power balance of the building while maintain the grid exchange power is distributed in a probabilistic security controllable interval such that the building turns out to be a grid-friendly building. The case study is tested on a smart building with random renewable power injection and flowing EVs, civil electric water heaters (EWHs) thermostatically controlled loads and the simulations results shows the effectiveness of the proposed DR control algorithms.

The optimal strategy estimation of random evolutionary Boolean games (REBGs) is discussed in this article. First, using the minimum mean square error criterion, the optimal strategy estimator is proposed for REBGs. Then, a matrix approach is developed to calculate the optimal strategy estimator by the aid of a semitensor product of matrices, which includes the prediction matrix, updating distribution, and strategy iterative formula. Finally, an elucidative example is included to show the obtained results are valid.

This article aims to stabilize probabilistic Boolean networks (PBNs) via a novel pinning control strategy. In a PBN, the state evolution of each gene switches among a collection of candidate Boolean functions with preassigned probability distributions, which govern the activation frequency of each Boolean function. Due to the existence of stochasticity, the mode-independent pinning controller might be disabled. Thus, both mode-independent and mode-dependent pinning controller are required here. Moreover, a criterion is derived to determine whether mode-independent controllers are applicable while the pinned nodes are given. It is worth pointing out that this pinning control is based on the$n\times n$network structure rather than$2^{n} \times 2^{n}$state transition matrix. Therefore, compared with the existing results, this pinning control strategy is more practicable and has the ability to handle large-scale networks, especially sparsely connected networks. To demonstrate the effectiveness of the designed control scheme, a PBN that describes the mammalian cell-cycle encountering a mutated phenotype is discussed as a simulation.

In this article, pinning control has been applied to stabilize a kind of stochastic network with finite states called probabilistic logical networks (PLNs). First, the solvability of pinning controllers, including the selection of pinning nodes and the corresponding control design, is addressed to guarantee the stabilization of PLNs. Then, based on the complete matrices set, one necessary and sufficient condition is obtained for PLNs to be stabilized by exact p nodes. In addition, an algorithm is presented for obtaining the minimal number of pinning nodes and how exact they are. As an application, our algorithm is used to calculate the minimal number of pinning nodes for the stabilization of logical networks (LNs). Examples are given to illustrate the process of choosing pinning nodes and show the efficiency of the obtained results.

Security control aims to guarantee the consensus of multiagent systems (MASs) in the presence of the denial-to-service attacker. Most of the existing distributed controllers are invalid during the attack interval due to the paralyzed communication channels. In order to overcome this difficulty, a novel hybrid distributed control protocol is designed. Here, the controller uses the latest information saved in the buffers in the presence of malicious attacks, which will further enhance the security of MASs. Some sufficient conditions on the coupled strength and attack parameters are derived to achieve the leader-following consensus of MASs. Furthermore, we estimate the upper bounds of denial-of-service (DoS) frequency and DoS duration which the MASs can tolerate before losing consensus. Notice that we also reduce the computational complexity via the property of the Kronecker product. Besides, an observer-based model is proposed and the corresponding consensus criterion is established to reduce the effects of attackers on the controller. Finally, the efficiency of our theoretical results is illustrated by a numerical example.

This article focuses on a distributed optimization problem subject to partial-impact cost functions that relates to two decision variable vectors. To this end, two algorithms are presented with the aim of solving the considered optimization problem in a structure fashion and in a gradient fashion, respectively. Furthermore, a connection between the equilibrium of the induced algorithm and the involved optimization problem is established, with the aid of the tools from nonsmooth analysis and change of coordinate theorem. Two numerical examples with practical significance are given to demonstrate the efficiency of the designed algorithm.

Network security issues are significant for cyber-physical systems while existing wireless networks are vulnerable to cyber-attacks. This paper proposes a novel detector for stealthy attacks in distributed consensus-based filtering, which has fewer objects to detect and thus can reduce the time consumption of the detector. Based on the proposed detector, we can analyze the estimated performance of the distributed estimator under a stealthy attack. The purpose of this study is to analyze the properties and performance of the estimator equipped with the proposed detector depending on the adversary’s available resources. First, we study the sufficient condition for distributed state estimation to be resilient based on the assumption that the adversary has sufficient resources. With limited adversary resources, the optimal Kalman gain can be obtained by minimizing state estimation error covariance. Furthermore, a sufficient condition is presented to guarantee the convergence of the estimation error covariance in the estimator equipped with the proposed detector. Finally, a simulation example is provided to demonstrate the effect of the detector on the distributed estimator.

In the brief, delayed impulsive control is investigated for the synchronization of chaotic neural networks. In order to overcome the difficulty that the delays in impulsive control input can be flexible, we utilize the concept of average impulsive delay (AID). To be specific, we relax the restriction on the upper/lower bound of such delays, which is not well addressed in most existing results. Then, by using the methods of average impulsive interval (AII) and AID, we establish a Lyapunov-based relaxed condition for the synchronization of chaotic neural networks. It is shown that the time delay in impulsive control input may bring a synchronizing effect to the chaos synchronization. Furthermore, we use the method of linear matrix inequality (LMI) for designing average-delay impulsive control, in which the delays satisfy the AID condition. Finally, an illustrative example is given to show the validity of the derived results.

In this article, the finite-time synchronization (FTSYN) of a class of quaternion-valued neural networks (QVNNs) with discrete and distributed time delays is studied. Furthermore, the FTSYN and fixed-time synchronization (FIXSYN) of the QVNNs without time delay are investigated. Different from the existing results, which used decomposition techniques, by introducing an improved one-norm, we use a direct analytical method to study the synchronization problems. Incidentally, several properties of one-norm of the quaternion are analyzed, and then, three effective controllers are proposed to synchronize the drive and response QVNNs within a finite time or fixed time. Moreover, efficient criteria are proposed to guarantee that the synchronization of QVNNs with or without mixed time delays can be realized within a finite and fixed time interval, respectively. In addition, the settling times are reckoned. Compared with the existing work, our advantages are mainly reflected in the simpler Lyapunov analytical process and more general activation function. Finally, the validity and practicability of the conclusions are illustrated via four numerical examples.

This article studies the state estimation for probabilistic Boolean networks via observing output sequences. Detectability describes the ability of an observer to uniquely estimate system states. By defining the probability of an observed output sequence, a new concept called detectability measure is proposed. The detectability measure is defined as the limit of the sum of probabilities of all detectable output sequences when the length of output sequences goes to infinity, and it can be regarded as a quantitative assessment of state estimation. A stochastic state estimator is designed by defining a corresponding nondeterministic stochastic finite automaton, which combines the information of state estimation and probability of output sequences. The proposed concept of detectability measure further performs the quantitative analysis on detectability. Furthermore, by defining a Markov chain, the calculation of detectability measure is converted to the calculation of the sum of probabilities of certain specific states in Markov chain. Finally, numerical examples are given to illustrate the obtained theoretical results.

Two synchronization problems, synchronization with probability one and synchronization in probability, are investigated for an array of coupled probabilistic Boolean networks (CPBNs). Compared with the former one, the in-probability problem considers a more general situation, in which synchronization can be achieved with a positive probability, instead of strictly 100%. It reflects the intrinsic randomness of biological systems. For both problems, some necessary and sufficient conditions are proposed, based on which two feasible algorithms are presented for checking two kinds of synchronization, respectively. CPBNs can be seemed as a combination of coupled Boolean networks (CBNs) with assigned probabilities. There are also detailed discussions on the impact of the synchronism of CBNs on the two addressed synchronization problems. The existence of invariant synchronization subsets is studied, which deepens our understanding on the difference and difficulty of these problems. Finally, numerical simulations show the effectiveness of the theoretical results.

This paper proposes two kinds of algorithms to achieve privacy-preserving consensus of multi-agent systems over undirected graphs via node decomposition mechanism and homomorphic cryptography technique. Based on the number of neighboring nodes ( |\mathscr Ni|), every agent is decomposed into |\mathscr Ni| subagents, which are connected as a chain graph. Note that every subagent connects one and only one non-homologous subagent (generated by different agents). Information interaction between non-homologous subagents is encrypted by a homomorphic cryptography algorithm, and homologous subagents exchange information directly. In this regard, the proposed node decomposition mechanism enhances the privacy of the initial values without increasing the computational complexity of encryption. The first privacy-preserving algorithm can achieve the accurate average consensus, which means that the agreement value of every subagent is consistent with the original average consensus value. The second algorithm studies the privacy-preserving scaled consensus problem without a priori knowledge about the underlying graph. Although the final convergence values of subagents do not keep exactly the same, homologous subagents can compute the original group decision value by resorting to the product of the limit value and agent's degree. Importantly, this algorithm also guarantees the privacy of group decision value of the whole system. Besides, it is proved that the privacy of the initial value can be preserved if the agent has at least one neutral neighbor.

The stabilization problem of Boolean control networks (BCNs) under pinning control is investigated in this article, and the set of pinned nodes is minimized. A BCN is a Boolean network with Boolean control inputs in it. When the given BCNs cannot realize stabilization under existing Boolean control inputs, pinning control strategy is introduced to make the BCNs achieve stabilization. The Warshall algorithm is introduced to verify the stabilizability of BCNs, then novel computational feasible algorithms are developed to design the minimum number pinning controller for the system. By using our method, the minimum set of pinned nodes can be found with relatively low computational complexity. Finally, the theoretical result is validated using a biological example.

In this article, synchronization problem in an array of output-coupled Boolean control networks (BCNs) is studied by using event-triggered sampled feedback control. Algebraic forms of an array of output-coupled BCNs are presented via the semitensor product (STP) of matrices. Based on the algebraic forms, a necessary and sufficient condition is obtained for the synchronization of an array of output-coupled BCNs. Furthermore, an algorithm is proposed to design event-triggered sampled feedback controllers. Finally, the obtained results are well illustrated by numerical examples.

This article studies the constrained optimization problems in the quaternion regime via a distributed fashion. We begin with presenting some differences for the generalized gradient between the real and quaternion domains. Then, an algorithm for the considered optimization problem is given, by which the desired optimization problem is transformed into an unconstrained setup. Using the tools from the Lyapunov-based technique and nonsmooth analysis, the convergence property associated with the devised algorithm is further guaranteed. In addition, the designed algorithm has the potential for solving distributed neurodynamic optimization problems as a recurrent neural network. Finally, a numerical example involving machine learning is given to illustrate the efficiency of the obtained results.

This article studies the stability in probability of probabilistic Boolean networks and stabilization in the probability of probabilistic Boolean control networks. To simulate more realistic cellular systems, the probability of stability/stabilization is not required to be a strict one. In this situation, the target state is indefinite to have a probability of transferring to itself. Thus, it is a challenging extension of the traditional probability-one problem, in which the self-transfer probability of the target state must be one. Some necessary and sufficient conditions are proposed via the semitensor product of matrices. Illustrative examples are also given to show the effectiveness of the derived results.

Analysis and design of steady states representing cell types, such as cell death or unregulated growth, are of significant interest in modeling genetic regulatory networks. In this article, the steady-state design of large-dimensional Boolean networks (BNs) is studied via model reduction and pinning control. Compared with existing literature, the pinning control design in this article is based on the original node's connection, but not on the state-transition matrix of BNs. Hence, the computational complexity is dramatically reduced in this article from O(2n× 2n) to O(2 × 2'), where n is the number of nodes in the large-dimensional BN and r <; n is the largest number of in-neighbors of the reduced BN. Finally, the proposed method is well demonstrated by a T-LGL survival signaling network with 18 nodes and a model of survival signaling in large granular lymphocyte leukemia with 29 nodes. Just as shown in the simulations, the model reduction method reduces 99.98% redundant states for the network with 18 nodes, and 99.99% redundant states for the network with 29 nodes.

This article investigates the output regulation problem of probabilistic$k$-valued logical systems with delays by an intermittent control scheme. Two types of event-triggered control are designed via semi-tensor product (STP) of matrices. According to the algebraic state-space representation of probabilistic$k$-valued systems with delays, the problem is transformed into the existence of solutions of algebraic equations. Then we obtain the sufficient and necessary condition for the output regulation problem of probabilistic$k$-valued logical systems with delays. Two types of approaches are given to design the event-triggered control laws. Eventually, two exemplifications are provided to explain the effectiveness and utility of the acquired results.

Significant attention has been paid to the bipartite consensus (BC) problem of multiagent systems (MASs) with antagonistic interactions. In many practical applications, the convergence speed is very important. In this article, we focus on the finite-time BC (FTBC) problems of MASs with detail-balanced antagonistic interactions. First, two FTBC protocols are designed and expressed in a unified form. Then, by taking advantage of some recent findings on network stability, we obtain theoretical results to guarantee that the states of all agents reach agreement in finite time under our proposed protocols. Finally, the effectiveness and validity of the main theoretical results are demonstrated via two numerical examples.

In this paper, we study the stabilization and finite-time stabilization of probabilistic Boolean control networks (PBCNs). A complete family of reachable sets is defined first, based on which, feedback stabilization conditions are obtained. Then a way to find all possible state feedback controllers are presented for the stabilization of PBCNs accordingly. Moreover, it has been stated that the approach in this paper can also be applied to finite-time stabilization via some changes in the construction of set sequence. Finally, an evolutionary networked game is given as an example to illustrate the efficiency of the obtained results.

We aim to further study the global stability of Boolean control networks (BCNs) under aperiodic sampled-data control (ASDC). According to our previous work, it is known that a BCN under ASDC can be transformed into a switched Boolean network (SBN), and further global stability of the BCN under ASDC can be obtained by studying the global stability of the transformed SBN. Unfortunately, since the major idea of our previous work is to use stable subsystems to offset the state divergence caused by unstable subsystems, the SBN considered has at least one stable subsystem. The central thought in this paper is that switching behavior also has good stabilization; i.e., the SBN can also be stable with appropriate switching laws designed, even if all subsystems are unstable. This is completely different from that in our previous work. Specifically, for this case, the dwell time (DT) should be limited within a pair of upper and lower bounds. By means of the discretized Lyapunov function and DT, a sufficient condition for global stability is obtained. Finally, the above results are demonstrated by a biological example.

In this paper, the stabilization problem of the Boolean network (BN) with stochastic disturbances via pinning control has been investigated. The necessary and sufficient conditions are given for robust stabilization of a BN with stochastic disturbances. Then, pinning control is considered to stabilize a BN with stochastic disturbances. An algorithm is given to obtain a new stable system and the pinning control, including the pinned nodes, control design, and control adding, is also solved. Finding the minimal number of pinned nodes is further analyzed. The necessary and sufficient conditions are obtained for the solvability of pinning control, based on which some matrices sets are constructed which leads to the necessary and sufficient conditions of pinning t nodes. Furthermore, an algorithm is introduced to search the minimal number of pinned nodes and what exactly they are, which will reduce the computational burden. Examples are given to illustrate the efficiency of the obtained results.

This article investigates global exponential synchronization almost surely (GES a.s.) of complex networks (CNs) with node delay and switching topology. By introducing transition probability (TP) and mode-dependent average dwell time (MDADT) to the switching signal, the considered model is more practical than the systems with average dwell-time (ADT) switching. Controllers with both impulsive effects and actuator fault feedback are considered. New analytical techniques are developed to obtain sufficient conditions to guarantee the GES a.s. Different from the existing results on the synchronization of switched systems, our results show that the GES a.s. can still be achieved even in the case that the upper bound of the dwell time (DT) of uncontrolled nodes is very large and the lower bound of the DT of controlled nodes is very small. Numerical examples demonstrate the effectiveness and the merits of the theoretical analysis.

In this brief, we investigate the robustness of outputs with respect to disturbances for Boolean control networks (BCNs) by semi-tensor product (STP) of matrices. First, BCNs are converted into the corresponding algebraic forms by STP, then two sufficient conditions for the robustness are derived. Moreover, the corresponding permutation system and permutation graph are constructed. It is proven that if there exist controllers such that the outputs of permutation systems are robust with respect to disturbances, then there must also exist controllers such that the outputs of the corresponding original systems achieve robustness with respect to disturbances. One effective method is proposed to construct controllers to achieve robustness. Examples are also provided to illustrate the correctness of the obtained results.

In this paper, the output feedback set stabilization problem for Boolean control networks (BCNs) is investigated with the help of the semi-tensor product (STP) tool. The concept of output feedback control invariant (OFCI) subset is introduced, and novel methods are developed to obtain the OFCI subsets. Based on the OFCI subsets, a technique, named spanning tree method, is further introduced to calculate all possible output feedback set stabilizers. An example concerning lac operon for the bacterium Escherichia coli is given to illustrate the effectiveness of the proposed method. This technique can also be used to solve the state feedback (set) stabilization problem for BCNs. Compared with the existing results, our method can dramatically reduce the computational cost when designing all possible state feedback stabilizers for BCNs.

This paper proposes a quaternion-valued one-layer recurrent neural network approach to resolve constrained convex function optimization problems with quaternion variables. Leveraging the novel generalized Hamilton-real (GHR) calculus, the quaternion gradient-based optimization techniques are proposed to derive the optimization algorithms in the quaternion field directly rather than the methods of decomposing the optimization problems into the complex domain or the real domain. Via chain rules and Lyapunov theorem, the rigorous analysis shows that the deliberately designed quaternion-valued one-layer recurrent neural network stabilizes the system dynamics while the states reach the feasible region in finite time and converges to the optimal solution of the considered constrained convex optimization problems finally. Numerical simulations verify the theoretical results.

Event-triggering strategy is a control implementation technique which intends to minimizing resource usage while achieving the acceptable performance of the closed-loop system. In this paper, an event-triggered sliding mode control (SMC) is designed for attitude stabilization of a rigid spacecraft subject to external disturbances and model uncertainties. A semi-global event-triggering strategy is proposed for SMC to keep the system trajectory in the vicinity of a proposed sliding surface. Since in this sliding surface, the sliding mode is asymptotic stable, the trajectories of the attitude control system remain ultimately bounded under the circumstance of disturbances and uncertainties. Moreover, the given event-triggered control implementation is only dependent on the angular velocity at sampling instant and triggering strategy with Zeno phenomenon can be avoided. Some numerical simulations are shown to illustrate the availability of the obtained results.

This paper studies the set stabilization of Boolean control networks (BCNs) under sampled-data state feedback control (SDSFC). The main research content is divided into two parts. First, the topological structure of BCNs under given SDSFC is investigated. The fixed point and sampled cycle are defined, respectively. It is found that sampled cycles allow elements to be repeated and not every element can be regarded as an initial state, and this is quite different from conventional cycles of BCNs. A theorem is presented to calculate the number of fixed points and an algorithm is given to find all fixed points and sampled cycles. Second, the set stabilization problem of BCNs by SDSFC is investigated based on the sampled point set and the sampled point control invariant set (SPCIS). A necessary and sufficient condition is derived for the global set stabilization of BCNs by SDSFC, and further sampled-data state feedback controllers are also designed. The interesting thing is that if a state enters the SPCIS as an unsampled point, then it may run out of the given set again, which is in sharp contrast to conventional BCNs. Finally, an example is given to illustrate the efficiency of the obtained results.

In this paper, we investigate the sampled-data state feedback control (SDSFC) for the synchronization of Boolean control networks (BCNs) under the configuration of drive-response coupling. Necessary and sufficient conditions for the complete synchronization of BCNs are obtained by the algebraic representations of logical dynamics. Based on the analysis of the sampling periods, we establish an algorithm to guarantee the synchronization of drive-response coupled BCNs by SDSFC. An example is given to illustrate the significance of the obtained results.

This paper studies pinning controllers for activation output tracking (AOT) of Boolean network under one-bit perturbation, based on the semitensor product of matrices. First, the definition of AOT with respect to an activation number is presented, where the activation number means the number of active outputs whose logical variables are 1 s. Then, several criteria are established for AOT issue. Further, the impact of one-bit perturbation on AOT is studied, where one-bit perturbation means that only one logical function has one-bit change of its truth table by flipping the value from 1 to 0 or 0 to 1. In addition, if a one-bit perturbation is a valid perturbation on AOT, an output feedback pinning control is designed to recover AOT. The obtained results are effectively illustrated by a D. melanogaster segmentation polarity gene network and a reduced signal transduction network.

In real systems, most of the biological functionalities come from the fact that the connections are not active all the time. Based on the fact, temporal Boolean networks (TBNs) are proposed in this paper, and the fast-time stability is analyzed via semi-tensor product (STP) of matrices and incidence matrices. First, the algebraic form of a TBN is obtained based on the STP method, and one necessary and sufficient condition for global fast-time stability is presented. Moreover, incidence matrices are used to obtain several sufficient conditions, which reduce the computational complexity from O(n2n) (exponential type) to O(n4) (polynomial type) compared with the STP method. In addition, the global fast-time stabilization of TBNs is considered, and pinning controllers are designed based on the neighbors of controlled nodes rather than all the nodes. Finally, the local fast-time stability of TBNs is considered based on the incidence matrices as well. Several examples are provided to illustrate the effectiveness of the obtained results.

The asymptotic synchronization of coupled reaction-diffusion neural networks with proportional delay and Markovian switching topologies is considered in this brief where the diffusion space does not need to contain the origin. The main objectives of this brief are to save communication resources and to reduce the conservativeness of the obtained synchronization criteria, which are carried out from the following two aspects: 1) mode-dependent quantized control technique is designed to reduce control cost and save communication channels and 2) Wirtinger inequality is utilized to deal with the reaction-diffusion terms in a matrix form and reciprocally convex technique combined with new Lyapunov-Krasovskii functional is used to derive delay-dependent synchronization criteria. The obtained results are general and formulated by linear matrix inequalities. Moreover, combined with an optimal algorithm, control gains with the least magnitude are designed.

This technical correspondence considers finite-time synchronization of dynamical networks by designing aperiodically intermittent pinning controllers with logarithmic quantization. The control scheme can greatly reduce control cost and save both communication channels and bandwidth. By using multiple Lyapunov functions and convex combination techniques, sufficient conditions formulated by a set of linear matrix inequalities are derived to guarantee that all the node systems are synchronized with an isolated trajectory in a finite settling time. Compared with existing results, the main characteristics of this paper are twofold: 1) quantized controller is used for finite-time synchronization and 2) the designed multiple Lyapunov functions are strictly decreasing. An optimal algorithm is proposed for the estimation of settling time. Numerical simulations are provided to demonstrate the effectiveness of the theoretical analysis.

This paper investigates the synchronization problem for the realization-dependent probabilistic Boolean networks (PBNs) coupled unidirectionally in the drive-response configuration. The realization of the response PBN is assumed to be uniquely determined by the realization signal generated by the drive PBN at each discrete time instant. First, the drive-response PBNs are expressed in their algebraic forms based on the semitensor product method, and then, a necessary and sufficient condition is presented for the synchronization of the PBNs. Second, by resorting to a newly defined matrix operator, the reachable set from any initial state is expressed by a column vector. Consequently, an easily computable algebraic criterion is derived assuring the synchronization of the drive-response PBNs. Finally, three illustrative examples are employed to demonstrate the applicability and usefulness of the developed theoretical results.

In this brief, we first study the normalization of dynamic-algebraic Boolean networks (DABNs). A new expression for the normalized DABNs is obtained. As applications of this result, the solvability and uniqueness of the solution to DABNs are then investigated. Necessary and sufficient conditions for the solvability and the uniqueness are obtained. In addition, pinning control to ensure the solvability and uniqueness of the solution to DABNs is also studied. Numerical examples are given to illustrate the efficiency of the proposed results.

In this brief, we study the delayed feedback stabilization problem for Boolean control networks (BCNs) with state delay. Using the semi-tensor product of matrices, some necessary and sufficient conditions are obtained. For the stabilization of BCNs, detailed procedure to construct the feedback controllers is also presented. We further derive the number of different feedback controllers, which can successfully stabilize the BCN in a finite time. Finally, an illustrative example is presented to show the effectiveness of our method.

In this paper, we investigate the global stability of quaternion-valued neural networks (QVNNs) with time-varying delays. On one hand, in order to avoid the noncommutativity of quaternion multiplication, the QVNN is decomposed into four real-valued systems based on Hamilton rules: $ij=-ji=k,~jk=-kj=i$ , $ki=-ik=j$ , $i^{2}=j^{2}=k^{2}=ijk=-1$ . With the Lyapunov function method, some criteria are, respectively, presented to ensure the global $\mu $ -stability and power stability of the delayed QVNN. On the other hand, by considering the noncommutativity of quaternion multiplication and time-varying delays, the QVNN is investigated directly by the techniques of the Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) where quaternion self-conjugate matrices and quaternion positive definite matrices are used. Some new sufficient conditions in the form of quaternion-valued LMI are, respectively, established for the global $\mu $ -stability and exponential stability of the considered QVNN. Besides, some assumptions are presented for the two different methods, which can help to choose quaternion-valued activation functions. Finally, two numerical examples are given to show the feasibility and the effectiveness of the main results.

This paper is concerned with the exponential synchronization issue of general chaotic neural networks subject to nonuniform sampling and control packet missing in the frame of the zero-input strategy. Based on this strategy, we make use of the switched system model to describe the synchronization error system. First, when the missing of control packet does not occur, an exponential stability criterion with less conservatism is established for the resultant synchronization error systems via a superior time-dependent Lyapunov functional and the convex optimization approach. The characteristics induced by nonuniform sampling can be used to the full because of the structure and property of the constructed Lyapunov functional, that is not necessary to be positive definite except sampling times. Then, a criterion is obtained to guarantee that the general chaotic neural networks are synchronous exponentially when the missing of control packet occurs by means of the average dwell-time technique. An explicit expression of the sampled-data static output feedback controller is also gained. Finally, the effectiveness of the proposed new design methods is shown via two examples.

In this paper, the problem of event-based synchronization of heterogeneous complex networks is investigated. Specifically, the influence of transmission delays on event-based synchronization is considered. The designed distributed controller for each nonidentical node in heterogeneous network includes reference generator (RG) and robust regulator. Event-based communication protocol is utilized to ensure the synchronization among the identical RGs and target leader. Meanwhile, the interevent intervals are lower bounded by a positive constant. Furthermore, the proposed high-gain output feedback and adaptive control law guarantee that all nonidentical nodes converge to their RGs. Based on these two steps, which are coincided with the separation principle, nonidentical nodes can track the target leader. In addition, theoretical results are demonstrated by a numerical example.

This paper addresses the partial synchronization problem for the interconnected Boolean networks (BNs) via the semi-tensor product (STP) of matrices. First, based on an algebraic state space representation of BNs, a necessary and sufficient criterion is presented to ensure the partial synchronization of the interconnected BNs. Second, by defining an induced digraph of the partial synchronized states set, an equivalent graphical description for the partial synchronization of the interconnected BNs is established. Consequently, the second partial synchronization criterion is derived in terms of adjacency matrix of the induced digraph. Finally, two examples (including an epigenetic model) are provided to illustrate the efficiency of the obtained results.

This paper investigates the controllability and synchronization problems for identical-hierarchy mixed-valued logical control networks. The logical network considered is hierarchical, and Boolean network is a special case of logical network. Here, identical-hierarchy means that there are identical number of nodes in each layer of logical network and corresponding nodes have the same dimension for any two layers of logical networks. Meanwhile, in each layer of logical networks, the dimensions of nodes are distinct, and it is called a mixed-valued logical network. First, the controllability problem is investigated and two notions of controllability are presented, i.e., group-controllability and simultaneously-controllability. By resorting to Perron-Frobenius theorem, some necessary and sufficient criteria are obtained to guarantee group-controllability and simultaneously-controllability, respectively. Second, based on the algebraic representation of the studied model, synchronization problems are analytically discussed for two types of controls, i.e., free control sequences and state-output feedback control. Finally, two numerical examples are presented to show the validness of our main results.

In this letter, we investigate the sampled-data state feedback control (SDSFC) problem of Boolean control networks (BCNs). Some necessary and sufficient conditions are obtained for the global stabilization of BCNs by SDSFC. Different from conventional state feedback controls, new phenomena observed the study of SDSFC. Based on the controllability matrix, we derive some necessary and sufficient conditions under which the trajectories of BCNs can be stabilized to a fixed point by piecewise constant control (PCC). It is proved that the global stabilization of BCNs under SDSFC is equivalent to that by PCC. Moreover, algorithms are given to construct the sampled-data state feedback controllers. Numerical examples are given to illustrate the efficiency of the obtained results.

This paper addresses robust multiobjective identification of driver nodes in the neuronal network of a cat's brain, in which uncertainties in determination of driver nodes and control gains are considered. A framework for robust multiobjective controllability is proposed by introducing interval uncertainties and optimization algorithms. By appropriate definitions of robust multiobjective controllability, a robust nondominated sorting adaptive differential evolution (NSJaDE) is presented by means of the nondominated sorting mechanism and the adaptive differential evolution (JaDE). The simulation experimental results illustrate the satisfactory performance of NSJaDE for robust multiobjective controllability, in comparison with six statistical methods and two multiobjective evolutionary algorithms (MOEAs): nondominated sorting genetic algorithms II (NSGA-II) and nondominated sorting composite differential evolution. It is revealed that the existence of uncertainties in choosing driver nodes and designing control gains heavily affects the controllability of neuronal networks. We also unveil that driver nodes play a more drastic role than control gains in robust controllability. The developed NSJaDE and obtained results will shed light on the understanding of robustness in controlling realistic complex networks such as transportation networks, power grid networks, biological networks, etc.

This brief investigates the partial and complete synchronization of two Boolean control networks (BCNs). Necessary and sufficient conditions for partial and complete synchronization are established by the algebraic representations of logical dynamics. An algorithm is obtained to construct the feedback controller that guarantees the synchronization of master and slave BCNs. Two biological examples are provided to illustrate the effectiveness of the obtained results.

Communication constraints, which may lead to the degradation of performance, are common and unavoidable in a real-world network. In this paper, two kinds of communication constraints are considered during the process of information transmission in Takagi-Sugeno (TS) fuzzy complex network: 1) partial couplings, where only some part of nodes' state information can be transmitted and the channel matrices are introduced to reflect such a phenomenon; and 2) discrete-time couplings, where the nodes' information are sampled at certain time instants. This is the first time when both communication constraints are simultaneously considered in fuzzy complex networks. Compared with the perfect communication, much less information is available for synchronization. To overcome this difficulty, a regrouping method is employed to reconstruct the fuzzy network. The concise conditions are then proposed to ensure pinning synchronization of fuzzy complex networks with partial and discrete-time couplings. Simulation examples are also provided to demonstrate the effectiveness of the theoretical results.

This paper is concerned with the cluster synchronization in finite time for a class of complex networks with nonlinear coupling strengths and probabilistic coupling delays. The complex networks consist of several clusters of nonidentical discontinuous systems suffered from uncertain bounded external disturbance. Based on the Takagi-Sugeno (T-S) fuzzy interpolation approach, we first obtain a set of T-S fuzzy complex networks with constant coupling strengths. By developing some novel Lyapunov functionals and using the concept of Filippov solution, some new analytical techniques are established to derive sufficient conditions ensuring the cluster synchronization in a setting time. In particular, this paper extends the pinning control strategies for networks with continuous-time dynamics to discontinuous networks. Numerical simulations demonstrate that the theoretical results are effective and the T-S fuzzy approach is important for relaxed results.

This paper is concerned with the problem of pinning synchronization of nonlinear dynamical networks with multiple stochastic disturbances. Two kinds of pinning schemes are considered: 1) pinned nodes are fixed along the time evolution and 2) pinned nodes are switched from time to time according to a set of Bernoulli stochastic variables. Using Lyapunov function methods and stochastic analysis techniques, several easily verifiable criteria are derived for the problem of pinning distributed synchronization. For the case of fixed pinned nodes, a novel mixed optimization method is developed to select the pinned nodes and find feasible solutions, which is composed of a traditional convex optimization method and a constraint optimization evolutionary algorithm. For the case of switching pinning scheme, upper bounds of the convergence rate and the mean control gain are obtained theoretically. Simulation examples are provided to show the advantages of our proposed optimization method over previous ones and verify the effectiveness of the obtained results.

This brief presents an analytical study of synchronization in an array of coupled deterministic Boolean networks (BNs) with time delay. Two kinds of models are considered. In one model, the outputs contain time delay, while in another one, the outputs do not. One restriction in this brief is that the state delay and output delay are restricted to be equal. By referring to the algebraic representations of logical dynamics and using the techniques of semitensor product of matrices, some necessary and sufficient conditions are derived for the synchronization of delay-coupled BNs. Examples including a practical epigenetic example are given for illustration.

In this paper, the robust synchronization problem of fuzzy complex dynamical networks is investigated. A fuzzy complex dynamical network is an extension to an uncertain complex dynamical network in which all sources of parametric uncertainties are modeled with fuzzy numbers, i.e., all nodes' dynamics are described by fuzzy differential equations (FDEs) that permit a better description of a real process occurring in the presence of inaccuracy. To resolve the synchronization problem, this paper introduces new adaptive and impulsive controllers in which globally exponential synchronization of fuzzy dynamical networks under easily verified conditions is guaranteed. Moreover, we propose an efficient method that helps to find certain suitable nodes to be impulsively controlled via pinning, noting that these nodes, in general, vary at distinct impulsive time instants. Therefore, by using adaptive controllers and applying impulsive controllers to only a small portion of nodes, the whole network will completely be synchronized to a certain objective state. Finally, two numerical examples are given to illustrate the effectiveness of the proposed controllers.

This paper is concerned with the distributed H∞filtering problem for a class of sensor networks with hybrid communication constraints. Three kinds of communications constraints are considered during the process of information transmission among the sensors: (i) the estimation of sensors needs to be sampled before transmitting; (ii) at each sampling instant, the packet dropouts would happen to the sampled data of sensors; (iii) the noise and disturbance exist. It should be noted that the constraints of sampled information and data packet dropouts would lead that less information can be employed for each sensor, which makes the filtering problem in sensor networks more challenging and practical. Some criteria concerning the connection gains are derived and used to design efficient distributed H∞filter to achieve the following objectives: (i) the filtering error system is exponentially mean-square stable in the absence of disturbance and noise; (ii) the prescribed H∞performance constraint is satisfied. A numerical example is utilized to illustrate the effectiveness of the theoretical results.

In this paper, a new control strategy is proposed for the synchronization of stochastic dynamical networks with nonlinear coupling. Pinning state feedback controllers have been proved to be effective for synchronization control of state-coupled dynamical networks. We will show that pinning impulsive controllers are also effective for synchronization control of the above mentioned dynamical networks. Some generic mean square stability criteria are derived in terms of algebraic conditions, which guarantee that the whole state-coupled dynamical network can be forced to some desired trajectory by placing impulsive controllers on a small fraction of nodes. An effective method is given to select the nodes which should be controlled at each impulsive constants. The proportion of the controlled nodes guaranteeing the stability is explicitly obtained, and the synchronization region is also derived and clearly plotted. Numerical simulations are exploited to demonstrate the effectiveness of the pinning impulsive strategy proposed in this paper.

In this paper, a general model of coupled neural networks with Markovian jumping and random coupling strengths is introduced. In the process of evolution, the proposed model switches from one mode to another according to a Markovian chain, and all the modes have different constant time-delays. The coupling strengths are characterized by mutually independent random variables. When compared with most of existing dynamical network models which share common time-delay for all modes and have constant coupling strengths, our model is more practical because different chaotic neural network models can have different time-delays and coupling strength of complex networks may randomly vary around a constant due to environmental and artificial factors. By designing a novel Lyapunov functional and using some inequalities and the properties of random variables, we derive several new sufficient synchronization criteria formulated by linear matrix inequalities. The obtained criteria depend on mode-delays and mathematical expectations and variances of the random coupling strengths as well. Numerical examples are given to demonstrate the effectiveness of the theoretical results, meanwhile right-continuous Markovian chain is also presented.

In this paper, fuzzy impulsive control is used for stabilization of chaotic systems based on the Takagi-Sugeno (T-S) model. The stability issue of the general nonlinear impulsive control system is first investigated via comparison criterion. Then, a novel impulsive control scheme is presented for chaotic systems based on the T-S fuzzy model. Some sufficient conditions are given to stabilize the T-S fuzzy model. Our results are proven to be less conservative theoretically and numerically. Moreover, we have also estimated the stable region of the impulsive interval. Finally, the proposed fuzzy impulsive control scheme is successfully applied to stabilize Rössler's system and Chua's circuit. The numerical simulations demonstrate the effectiveness and advantage of our main results.

This brief investigates globally exponential synchronization for linearly coupled neural networks (NNs) with time-varying delay and impulsive disturbances. Since the impulsive effects discussed in this brief are regarded as disturbances, the impulses should not happen too frequently. The concept of average impulsive interval is used to formalize this phenomenon. By referring to an impulsive delay differential inequality, we investigate the globally exponential synchronization of linearly coupled NNs with impulsive disturbances. The derived sufficient condition is closely related with the time delay, impulse strengths, average impulsive interval, and coupling structure of the systems. The obtained criterion is given in terms of an algebraic inequality which is easy to be verified, and hence our result is valid for large-scale systems. The results extend and improve upon earlier work. As a numerical example, a small-world network composing of impulsive coupled chaotic delayed NN nodes is given to illustrate our theoretical result.

The globally exponential synchronization problem for general dynamical networks is considered in this paper. One quantity will be distilled from the coupling matrix to characterize the synchronizability of the corresponding dynamical networks. The calculation of such a quantity is very convenient even for large-scale networks. The network topology is assumed to be directed and weakly connected, which implies that the coupling configuration matrix can be asymmetric, weighted, or reducible. This assumption is more consistent with the realistic network in practice than the constraint of symmetry and irreducibility. By using the Lyapunov functional method and the Kronecker product techniques, some criteria are obtained to guarantee the globally exponential synchronization of general dynamical networks. In addition, numerical examples, including small-world and scale-free networks, are given to demonstrate the theoretical results. It will be shown that our criteria are available for large-scale dynamical networks.

Pinning stabilization problem of linearly coupled stochastic neural networks (LCSNNs) is studied in this paper. A minimum number of controllers are used to force the LCSNNs to the desired equilibrium point by fully utilizing the structure of the network. In order to pinning control the LCSNNs to a certain desired state, only one controller is required for strongly connected network topology, and m controllers, which will be shown to be the minimum number, are needed for LCSNNs with m -reducible coupling matrix. The isolate node of the LCSNNs can be stable, periodic, or even chaotic. The coupling Laplacian matrix of the LCSNNs can be symmetric irreducible, asymmetric irreducible, or m-reducible, which means that the network topology can be strongly connected, weakly connected, or even unconnected. There is no constraint on the network topology. Some criteria are derived to judge whether the LCSNNs can be controlled in mean square by using designed controllers. The given criteria are expressed in terms of strict linear matrix inequalities, which can be easily checked by resorting to recently developed algorithm. Moreover, numerical examples including small-world and scale-free networks are also given to demonstrate that our theoretical results are valid and efficient for large systems.