This paper explores the issue of collision-free optimal tracking control of unmanned aerial vehicle (UAV) and unmanned ground vehicle (UGV) formation under Byzantine attacks. Based on collision-free margin and collision risk angle, a collision avoidance scheme for UAV-UGV swarms is proposed, which takes into account both external and internal aspects of the formation. Meanwhile, considering that the UAV-UGV swarm is susceptible to the propagation of incorrect neighbors’ information and false input signals (called Byzantine attacks), which is effectively reinterpreted as the management of unknown variables within the control inputs. Then, a barrier function and a control force direction function are introduced in the optimal performance index for collision avoiding with each system’s radius, and a collision-free optimal control strategy under the reinforcement learning (RL) algorithm is investigated. Furthermore, the neural network is utilized to model the Byzantine attacks and appropriate unknown factors arising from Hamilton-Jacobi-Bellman (HJB) equation, the actor and critic adaptive laws are presented in actor-critic-identifier architecture. Subsequently, a collision-free optimal tracking control scheme is proposed to ensure safe collaborative moving of the UAV-UGV formation under Byzantine attacks. Finally, simulations are performed to validate the effectiveness of the proposed approach.

Network Dismantling (ND) seeks to identify the smallest subset of nodes whose removal fragments a network into disconnected components. Traditional methods rely on fixed centrality heuristics or supervised models trained on synthetic data, often failing to generalize across diverse topologies. We introduce GRLND, a Graph Reinforcement Learning framework that enables fully unsupervised, structure-aware dismantling through end-to-end optimization. GRLND formulates ND as a single-step Markov Decision Process (MDP), where the action is a binary mask indicating the nodes to be removed-allowing the agent to generate a complete dismantling strategy in a single forward pass while accounting for the joint effect of multiple node removals. The framework combines a Graph Convolutional Network (GCN) for topological encoding with a stochastic policy trained via the REINFORCE algorithm. Additionally, we design a task-specific reward that balances connectivity disruption and removal sparsity, guiding the policy toward compact yet high-impact dismantling solutions. Experiments on both synthetic and real-world networks show that GRLND consistently outperforms classical heuristics and recent learning-based methods, achieving strong generalization without requiring labels or pretraining.

With the development of multimedia technology, online social media has become a major medium for people to access news, but meanwhile, it has also exacerbated the dissemination of multi-modal fake news. An automatic and efficient multi-modal fake news detection (MFND) method is urgently needed. Existing MFND methods usually conduct cross-modal information interaction at later stage, resulting in insufficient exploration of complementary information between modalities. Another challenge lies in the differences among news data from different domains, leading to the weak generalization ability in detecting news from various domains. In this work, we propose an efficient Cross-modal Prompt Learning with Semantic enhancement method for Domain-robust fake news detection (CPLSD). Specifically, we design an efficient cross-modal prompt interaction module, which utilizes prompt as medium to realize lightweight cross-modal information interaction in the early stage of feature extraction, enabling to exploit rich modality complementary information. We design a domain-general prompt generation module that can adaptively blend domain-specific news features to generate domain-general prompts, for improving the domain generalization ability of the model. Furthermore, an image semantic enhancement module is designed to achieve image-to-text translation, fully exploring the semantic discriminative information of the image modality. Extensive experiments conducted on three MFND benchmarks demonstrate the superiority of our proposed approach over existing state-of-the-art MFND methods.

This article explores the optimized tracking control problem of autonomous aerial vehicle (AAV) and autonomous ground vehicle (AGV) swarm with mismatched disturbances and Byzantine attacks. Unlike traditional AGV-AAV models with different orders, multiple internal and external disturbances within the physical structure are considered in a novel second-order AAV-AGV swarm, which constructs the mismatched disturbances. Since the external environment may induce the swarm to generate and propagate false signals (called Byzantine attacks) to its neighbors, this article reinterprets it as the management of unknown variables in the control inputs. Then, a reinforcement-learning-based approach is introduced to address the unknown control inputs generated by Byzantine attacks. In conjunction with the Hamilton-Jacobi–Bellman (HJB) equation, an adaptive actor-critic–identifier (ACI) structure is designed using the gradient descent method. With the unknown terms estimated by ACI, an optimal robust control strategy under mismatched disturbances is proposed, and a pivotal scaling technique is employed for formation stability analysis. Finally, simulations and experimental results are performed to demonstrate the efficacy of the proposed approach.

To achieve a high data rate while maintaining a low peak to average power ratio (PAPR), a novel generalized multi-level code-shifted differential chaos shift keying modulation system is proposed. In this system, both the reference and multiple data-bearing signals transmit data bits through code index modulations performed on the same set of Walsh codes, leading to enhanced utilization of indices and increased data rate. In addition, each data-bearing signal transmits one extra bit using differential chaos shift keying modulation. To mitigate high PAPR, discrete cosine spreading codes are employed to distinguish between the reference and data-carrying signals. Two receiver configurations are designed to balance low complexity and improved bit error rate performance. Bit error rate performances are analyzed and simulated under the additive white Gaussian noise and multipath Rayleigh fading channels. Finally, comparisons are made between the proposed and other CS-DCSK-based systems, which illustrates that our system can offer an increased data rate and superior bit error rate performance, along with a reduced PAPR.

Abstract To obtain better spectral efficiency and higher bit rate, a novel carrier index M‐ary differential chaos shift keying modulation scheme is proposed. In this system, part of subcarriers is assigned to the chaotic reference so that it can carry extra data bits through carrier index modulation, while one of the remaining subcarriers is activated to transmit the data‐bearing signal. In addition, M‐ary DCSK modulation is also applied to data‐bearing signals based on the constellation theory and Walsh codes. Theoretical bit error rate expressions are derived over the multipath Rayleigh fading and additive white Gaussian noise channels. Simulations and comparisons are performed with various combinations of chaotic sequence lengths, subcarrier numbers and constellation sizes. Results show that the proposed scheme can outperform other counterparts in both spectral efficiency and bit error rate performances.

Abstract A high‐data‐rate solution for M‐ary differential chaos shift keying (MDCSK) based on carrier index modulation is proposed in this paper. At the transmitter, the proposed system employs index selectors, Hilbert transform, and MDCSK encoders. Walsh codes are used for separating different data‐bearing wavelets. At the receiver, the proposed system adopts energy comparators and MDCSK detectors. The transmitted chaotic signals are duplicated for several times, and the averaging operation is performed on received signals to reduce noise. Theoretical bit error rate expressions are obtained over the AWGN and the multipath Rayleigh fading channels, respectively. Simulations and comparisons are performed to verify the effectiveness of the proposed scheme.

Recently, generative adversarial networks (GAN) have made remarkable progress, particularly with the advent of Contrastive Language-Image Pretraining (CLIP), which take image and text into a joint latent space, bridging the gap between these two modalities. Several impressive text-guided image editing methods based on GANs and CLIP have emerged. However, in these studies, most of them simply minimize the distance between the target image embedding and text embedding in the CLIP space, and take this objective as network's optimization goal, overlooking the real distance between them may be large. This may result in inability to accurately guide the editing process according to the text prompts and the changes in text-irrelevant attributes. To mitigate this issue, we propose a novel approach named CLIP with Mapping-Fusion Embedding (MFECLIP) for text-guided image editing, which comprises two components: the MFE Block and MFE Loss. Through the MFE Block, we obtain Mapping-Fusion Embedding (MFE), which can further eliminate the modality gap, and it can serve as a superior guide for editing process instead of the original text embedding. Based on contrastive learning, the MFE Loss is designed to achieve accurate alignment between the target image and text prompt. We have conducted extensive experiments on real datasets, CUB and Oxford, demonstrating the favorable performance of the proposed method.

Precisely knowing each instance’s position and extents is a critical first step in many biological applications. State-of-the-art techniques rely either on deep learning models designed to predict segmentation masks on each Region of Interest (RoI) or on classic active contour methods. The former struggles to precisely delineating boundaries and tends to output masks at low resolutions when the cells/nuclei are very irregular while the latter often needs good initialization and manual setting of parameters, thus limiting their usefulness. To bridge this gap, we introduce Snake R-CNN, a new level of the learnable active contour model that predict boundary on each RoI in a sequent way. To do so, for each RoI, we reformulate the contour deformation task in terms of a hidden state evolution problem and update the evolution process using energy minimization. We learn snake parameterizations per instance in an end-to-end manner, and demonstrate its effectiveness for contour inferences of various cell/nucleus types where consistently higher performances were obtained for comparison against state-of-the-arts.

Recently, most impressive Siamese network-based trackers are equipped with two independent branches: tracked object classification and bounding box regression. However, there is no tracking information exchange between them during the tracking optimization process. This may lead to the task-mismatch and accuracy inconsistency between both classification and regression branches during inference. To tackle the problems, we propose a novel Mutual Guidance (MG) strategy for visual object tracking, which constructs the bidirectional and complementary tracking information interaction to maintain the tracked object is well-classified to also be well-localized, between classification and regression branches. Specifically, the classification branch can guide the regression one to pay more attention to the sample with high classified scores, by re-weighting the regression loss with the classification confidence. Similarity, the regression branch also guides the classifier optimization process to focus on samples with larger IoU values. And then, the proposed Mutual Guidance is completed by a series of regularization designs on classification score and regression IoU, which dynamically re-assign the adaptive weights to the losses for each sample during the joint tracking optimization. The developed MG is generic and easy to be plugged into various tracking frameworks such as anchor-based, anchor-free based and transformer based, and boost their performance to some extent with negligible additional cost. In addition, we also develop an adaptive localization(L) branch selection scheme to further assist trackers, which determines proper localization branch for different trackers according to the difference in the way of discriminating positive and negative samples. Extensive experiments verify the effectiveness of MGL and its superiority against the state-of-the-art tracking modules on OTB100, GOT-10K, LaSOT, TrackingNet, UAV123, VOT2018 and VOT2019.

Most super-resolution methods are trained on datasets where high-resolution images and corresponding low-resolution images are obtained by the fixed degradation method. However, these external-based methods would fail to recover the detailed information of the test images if it could not be found in datasets. In this paper, we propose the momentum feature comparison network to generate the super-resolution image with rich texture information. Without the participation of high-resolution images in the training process, our method belongs to the completely unsupervised super-resolution method. A siamese structure with momentum update in generator is proposed to expand the content information of the low-resolution image and maintains the continuous consistency of intermediate feature maps. Furthermore, the results of two branches are fused through the feature fusion module to retain the global distribution of features and enhance local high-frequency details. The experimental results show that our method achieves great results compared with the state-of-the-art methods.

This article studies the multiagent bipartite consensus in networks with deterministic disturbances and antagonistic interactions. An observer-based output-feedback controller design is provided to guarantee the bipartite consensus with deterministic disturbances that satisfy the matching condition. Then, by considering that the bandwidths of communication channels are limited in practical systems, the event-triggered scenario of the proposed output controller for the bipartite consensus is further studied; the node-based broadcast updating fashion is utilized and the Zeno behavior is ruled out. Simulations are also offered to support the theoretical results of protocol designs.

This article concerns the robust consensus problem of continuous-time linear multiagent systems (MASs) with uncertainty and discrete-time measurement information, where the output measurement information is in the data-sampled form. Distributed output-feedback protocol with or without controller interaction is proposed for each agent. Specifically, the output-feedback protocol runs in continuous time with an output error correction term mixed with the discrete-time measurement information. The concrete algorithm is given for the construction of the feedback matrices. Then, by using the delay-input approach, sufficient conditions are provided for the robust consensus of this kind of MASs interacting over networks described by the directed graphs. Finally, numerical simulations are given to illustrate the theoretical results.

In this article, we refocus on the distributed observer construction of a continuous-time linear time-invariant (LTI) system, which is called the target system, by using a network of observers to measure the output of the target system. Each observer can access only a part of the component information of the output of the target system, but the consensus-based communication among them can make it possible for each observer to estimate the full state vector of the target system asymptotically. The main objective of this article is to simplify the distributed reduced-order observer design for the LTI system on the basis of the consensus communication pattern. For observers interacting on a directed graph, we first address the problem of the distributed reduced-order observer design for the detectable target system and provide sufficient conditions involving the topology information to guarantee the existence of the distributed reduced-order observer. Then, the dependence on the topology information in the sufficient conditions will be eliminated by using the adaptive strategy and so that a completely distributed reduced-order observer can be designed for the target system. Finally, some numerical simulations are proposed to verify the theoretical results.

This article focuses on the multiagent consensus disturbance rejection (MCDR) for groups of general linear individuals by using the distributed event-based adaptive control technique. Based on designing disturbance observers, event-driven control rules involving controllers and actuator updating rules are provided for networks of multiple individuals without and with input uncertainties; the updating rules rely on the state-dependent factor, the exponential decay threshold, and a tuning parameter. For both scenarios, the global information of network topologies is not required in the design and continuous communications between agents can be avoided.

This paper designed a pneumatic soft climbing robot by utilizing the high flexibility of soft materials. Capabilities of climbing and creeping through small spaces would rarely possible with a method based only on rigid links. At first, according to the drive mode of pneumatic networks, a model for soft climbing robots with different section having their independent stiffness was designed; afterwards, the analysis of visco-mechanical properties of robots at the contact surface were provided by using the method of minimum potential energy; on the basis, finite element analysis and experiment are given to analyze the climbing behaviors of the robot; finally, by employing 3-d printing and layer-by-layer casting, a prototype soft climbing robot was prepared to perform climbing experiments. The research is expected to provide a new method for monitoring complex unstructured environments.

In this paper, the robust coordination control of multi-agent systems (MASs) with uncertainties is considered, where the uncertainties include the external disturbances and the measurement noises as well as the unknown initial states. Motivated by the interval observer of single-agent systems, a distributed interval observer is designed for MASs communicating through a directed network which contains a directed spanning tree by using only the bounding information on the uncertainties and the output information, to implement the interval-valued state estimation on the absolute state of each agent. It also finds that the robust coordination control is a by-part of the distributed interval observer design of this kind of MASs. Moreover, a time-invariant transformation is used to perfect the distributed interval observer design. Finally, numerical simulations are proposed to verify the theoretical results.

This article focuses on the hybrid effects of memristor characteristics, time delay, and biochemical parameters on neural networks. First, we propose a novel neuron system with memristor and time delays in which the memristor is characterized by a smooth continuous cubic function. Second, the existence of equilibria of this type of neuron system is examined in the parameter space. Sufficient conditions that ensure the stability of equilibria and occurrence of pitchfork bifurcation are given for the memristor-based neuron system without delay. Third, some novel criteria of the addressed neuron system are constructed for guaranteeing the delay-dependent and delay-independent stability. The specific conditions are provided for Hopf bifurcations, and the properties of Hopf bifurcation are ascertained using the center manifold reduction and the normal form theory. Moreover, there exists a phenomenon of bistability for the delayed memristor-based neuron system having three equilibria. Finally, the effectiveness of the theoretical results is demonstrated by numerical examples.

This paper studies quasi-synchronization in networked heterogeneous harmonic oscillators. By introducing a leader, two distributed synchronization protocols are first proposed for heterogeneous networks by utilizing continuous real-time information and aperiodic sampled-data information. Then, the sufficient conditions on quasi-synchronization are established for heterogeneous networks coupled with nonidentical harmonic oscillators. It is found that each follower oscillator can converge to a bounded region of the leader by adopting either a continuous-time protocol or sampled-data protocol. The upper bound of the region is solved for networked heterogeneous harmonic oscillators. Finally, an electrical network is provided to illustrate the applicability of the theoretical results, and two examples are provided to illustrate the effectiveness of the sufficient criteria.

This article refocuses on the global coordination of networked systems with input saturation and external disturbances. With the help of a novel backstepping approach, a multihop relay control algorithm subject to a group of modified heterogenous saturation functions is constructed, in which the number of the hop is equal to the order of the networked system. It is proved that these modified heterogenous saturation functions can develop a global unsaturated control algorithm for each agent. Then, some sufficient and necessary conditions are provided for the global consensus of the connected networked systems with input saturation in the absence of external disturbances. In the presence of the input saturation and external disturbances, a sufficient condition irrelevant to the interactive network topology information is proposed for the global swarm of connected networked systems. Finally, numerical simulations are provided to verify the theoretical results.

Bifurcation control remains largely unresolved for fractional-order dynamical systems. This article addresses the optimal control issue of bifurcation for a delayed complex networks model with Caputo derivative, where the time delay is selected as the variable parameter. We first devise a fractional-order proportional-integral-derivative (PID) feedback synthesis for regulation of the Hopf bifurcation embedded in a delayed small-world network model with Caputo derivative. Dynamic stability criterion and Hopf bifurcation condition are obtained by carrying out the eigenvalue analysis of the controlled network. The stability range of the parameters of the PID control is evaluated completely for the small-world network. We can optimize the dynamics of stability and bifurcation of small-world networks by manipulating the gain parameters. Finally, we implement some simulations to show the performance of the presented PID scheme. The numerical simulations verify the advantage of the fractional PID controller in bifurcation control.

The functionalities, such as connectivity and communication capability of complex networks, are related to the number and length of paths between node pairs in the networks. In this paper, we propose a new path connectivity measure by considering the number and length of paths of the network (PCNL) to evaluate network path connectivity. By comparing the PCNL with the typical natural connectivity, we prove the effectiveness of the PCNL to measure the path connectivity of networks. Because of the importance of the shortest paths, we further propose the shortest paths connectivity measure (SPCNL) based on the number and length of the shortest paths. Then, we use edge-betweenness-based malicious attacks to study the relationship between the SPCNL and network topology in five types of networks. The results show that the SPCNLs of the networks have a significant corresponding relationship and similar changing trend with their network topology heterogeneities with the increase of the number of deleted edges. These findings mean that the SPCNL is positively correlated with the heterogeneity of the network topology, which provides a new perspective for designing complex networks with high path connectivity.

Different from image inpainting, image outpainting has relatively less context in the image center to capture and more content at the image border to predict. Therefore, classical encoder-decoder pipeline of existing methods may not predict the outstretched unknown content perfectly. In this paper, a novel two-stage siamese adversarial model for image extrapolation, named Siamese Expansion Network (SiENet) is proposed. Specifically, in two stages, a novel border sensitive convolution named adaptive filling convolution is designed for allowing encoder to predict the unknown content, alleviating the burden of decoder. Besides, to introduce prior knowledge to network and reinforce the inferring ability of encoder, siamese adversarial mechanism is designed to enable our network to model the distribution of covered long range feature as that of uncovered image feature. The results on four datasets has demonstrated that our method outperforms existing state-of-the-arts and could produce realistic results. Our code is released on https://github.com/nanjingxiaobawang/SieNet-Image-extrapolation.

Disconnecting impaired or suspicious nodes and rewiring to those reliable, adaptive networks have the potential to inhibit cascading failures, such as DDoS attack and computer virus. The weights of disconnected links, indicating the workload of the links, can be transferred or redistributed to newly connected links to maintain network operations. Distinctively different from existing studies focused on adaptive unweighted networks, this paper presents a new mean-field model to analyze the reliability of adaptive weighted networks against cascading failures. By taking mean-field approximation, we develop a new continuous-time Markov model to capture the propagations of cascading failures and the rewiring actions that individual nodes can take to bypass failed neighbors. We analyze the stability of the model to identify the critical conditions, under which the cascading failures can be eventually inhibited or would proliferate. The conditions are evaluated under different link weight distributions and rewiring strategies. Our model reveals that preferentially disconnecting suspicious peers with high weights can effectively inhibit virus and failures.

This article investigates distributed coordinated tracking problems of networked heterogeneous systems. Based on asynchronous sampling information, distributed sampled-data protocols are employed to realize leader-following synchronization and containment tracking in networked heterogeneous systems. In asynchronous sampled-data protocols, each node has different sampling instants with other nodes and only samples itself information at its own sampling instants. By utilizing the input-delay approach and Lyapunove-Krasovskii functional approach, some sufficient conditions for guaranteeing the coordinated tracking are presented. First, quasi-synchronization criteria are obtained for networked heterogeneous oscillator systems with a dynamic leader over the directed graph. Second, in the presence of multiple heterogeneous leaders for networked heterogeneous systems, sufficient conditions of quasi-containment tracking are derived. In a word, all followers can converge into a bounded level of convex hull spanned by the leader(s). The upper bounds of tracking errors are estimated for both quasi-synchronization and quasi-containment tracking. Finally, two numerical examples are given to verify the theoretical results.

In this paper, we present a distributed observer-type consensus controller design for general linear multiagent systems over directed digital networks with limited communication data rates. Considering that each agent can only exchange binary symbolic sequence with its neighbors due to bandwidth constraints, we adopt the probabilistic quantization approach in the distributed consensus controller design. Compared to the existing works, the main contribution is that we use distributed observer-type controllers to inhibit the impact of quantization noises in agent states. First, we study the observer-type protocols with total quantized communications, where the relative-state information of each agent is quantized. The quantized consensus can be achieved, and the upper bounds of steady-state errors in the mean-square sense are also characterized, which are related to the scale of networks, the control parameters, the quantization levels, and the structures of agents. Further, we extend the controller design based on total quantization to the partial quantization case where only the neighbors' information is quantized.

This paper is concerned with leader-following synchronization in a heterogeneous network coupled by a group of heterogeneous LC oscillators. Both the dynamics between the leader and each follower and the dynamics among the followers are nonidentical. A sampled-data-based protocol is proposed. The sufficient criteria for quasi-synchronization are derived based on the delayed input approach and the Lyapunov stability method. Furthermore, the quasi-synchronization error bound can be solved. Finally, simulations are given to illustrate the theoretical results.

It has been demonstrated in a large number of experimental results that small RNAs (sRNAs) play a vital role in gene regulation processes. Thus, the gene regulation process is dominated by sRNAs in addition to messenger RNAs and proteins. However, the regulation mechanism of sRNAs is not well understood and there are few models considering the effect of sRNAs. So it is of realistic biological background to include sRNAs when modeling gene networks. In this paper, sRNAs are incorporated into the process of gene expression and a new differential equation model is put forward to describe cyclic genetic regulatory networks with sRNAs and multiple delays. We mainly investigate the stability and bifurcation criteria for two cases: 1) positive cyclic genetic regulatory networks and 2) negative cyclic genetic regulatory networks. For a positive cyclic genetic regulatory network, it is revealed that there may exist more than one equilibrium and the multistability can appear. Sufficient conditions are established for the delay-independent stability and fold bifurcations. It is found that the dynamics of positive cyclic gene networks has no bearing on time delays, but depends on the biochemical parameters, the Hill coefficient and the equilibrium itself. For a negative cyclic genetic regulatory network, it is proved that there exists a unique equilibrium. Delay-dependent conditions for the stability are derived, and the existence of Hopf bifurcations is examined. Different from the delay-independent stability of positive gain networks, the stability of equilibrium is determined not only by the biochemical parameters, the Hill coefficient and the equilibrium itself, but also by the total delay. At last, three illustrative examples are provided to validate the major results.

Depth cameras have recently become popular and many vision problems can be better solved with depth information. But, how to integrate depth information into a visual tracker to overcome the challenges such as occlusion and background distraction is still underinvestigated in current literature on visual tracking. In this paper, we investigate a 3-D extension of a classical mean-shift tracker whose greedy gradient ascend strategy is generally considered as unreliable in conventional 2-D tracking. However, through careful study of the physical property of 3-D point clouds, we reveal that objects which may appear to be adjacent on a 2-D image will form distinctive modes in the 3-D probability distribution approximated by kernel density estimation, and finding the nearest mode using 3-D mean-shift can always work in tracking. Based on the understanding of 3-D mean-shift, we propose two important mechanisms to further boost the tracker's robustness: one is to enable the tracker to be aware of potential distractions and make corresponding adjustments to the appearance model; and the other is to enable the tracker to detect and recover from tracking failures caused by total occlusion. The proposed method is both effective and computationally efficient. On a conventional personal computer, it runs at more than 60 FPS without graphical processing unit acceleration.

Defence against cascading failures is of great theoretical and practical significance. A novel load capacity model with a tunable proportion is proposed. We take degree and clustering coefficient into account to redistribute the loads of broken nodes. The redistribution is local, where the loads of broken nodes are allocated to their nearest neighbours. Our model has been applied on artificial networks as well as two real networks. Simulation results show that networks get more vulnerable and sensitive to intentional attacks along with the decrease of average degree. In addition, the critical threshold from collapse to intact states is affected by the tunable parameter. We can adjust the tunable parameter to get the optimal critical threshold and make the systems more robust against cascading failures.

In this paper, we consider the problem of solving distributed constrained optimization over a multiagent network that consists of multiple interacting nodes in online setting, where the objective functions of nodes are time-varying and the constraint set is characterized by an inequality. Through introducing a regularized convex-concave function, we present a consensus-based adaptive primal-dual subgradient algorithm that removes the need for knowing the total number of iterations in advance. We show that the proposed algorithm attains an [where ] regret bound and an bound on the violation of constraints; in addition, we show an improvement to an regret bound when the objective functions are strongly convex. The proposed algorithm allows a novel tradeoffs between the regret and the violation of constraints. Finally, a numerical example is provided to illustrate the effectiveness of the algorithm.

Abstract In low signal‐to‐noise ratio (SNR) cases, the performance of spectrum sensing algorithms cannot meet the practical needs, which is a major problem faced by spectrum sensing technology in current cognitive radio field. Now, existing algorithms based on random matrix theory (RMT) have high sensing performance, but they require a large number of samples, which are very difficult to satisfy in practice. Free probability theory (FPT) is a main branch of RMT. It describes the asymptotic behavior of large random matrices and portrays a strong link between two matrices and their sum or product matrices. FPT can also be utilized to the digital communication system that can be modeled by random matrices and has been applied to spectrum sensing in simplified ideal channels, for example, additive white Gaussian noise channel. The most pivotal issue and difficulty of the FPT‐based methods is to set up and solve the asymptotic freeness equation corresponding to a specific communication model. In this paper, FPT‐based spectrum sensing schemes are proposed for some typical wireless communication systems, such as multiple‐input multiple‐output system, Rayleigh multipath fading system, and orthogonal frequency division multiplexing system. It is shown that the asymptotic freeness behavior of random matrices and the property of Wishart distribution can be used to assist spectrum sensing for these typical systems with low SNR and very limited samples. Simulation results demonstrate that compared with the existing RMT‐based spectrum detection methods, for example, the maximum and minimum eigenvalue detectors, the proposed FPT‐based schemes offer superior detection performance and are more robust to low SNR cases, especially for a small sample of observations. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, a fractional-order recurrent neural network is proposed and several topics related to the dynamics of such a network are investigated, such as the stability, Hopf bifurcations, and undamped oscillations. The stability domain of the trivial steady state is completely characterized with respect to network parameters and orders of the commensurate-order neural network. Based on the stability analysis, the critical values of the fractional order are identified, where Hopf bifurcations occur and a family of oscillations bifurcate from the trivial steady state. Then, the parametric range of undamped oscillations is also estimated and the frequency and amplitude of oscillations are determined analytically and numerically for such commensurate-order networks. Meanwhile, it is shown that the incommensurate-order neural network can also exhibit a Hopf bifurcation as the network parameter passes through a critical value which can be determined exactly. The frequency and amplitude of bifurcated oscillations are determined.

The state estimation problem is addressed in the paper for a complex dynamical network with stochastic noise in transmission channel. A new scheme based on integral observer approach is proposed for the complex dynamical network to estimate the network's states. It is demonstrated that the proposed scheme is effective under a noisy communication environment by using Lyapunov stability theory. A sufficient condition for complex dynamical network state estimation is derived in the form of a linear matrix inequality. It is demonstrated with the small world network and the scale-free network that the noise suppression can be achieved by using the proposed integral observer scheme.