This paper addresses two challenging issues in distributed Nash equilibrium seeking for a class of nonaffine, high-order nonlinear systems. The first lies in the complexity explosion that arises in adaptive feedback control when dealing with intricate system nonlinearities. The second concerns the oscillations caused by uncertain high-order nonaffine dynamics with unknown control directions. To overcome these challenges, a modified finite-time nonlinear tracking differentiator with linear damping components is established, settling down the high sensitivity of traditional filters. A unified framework is developed to handle input nonlinearities, including backlash-like hysteresis and dead zones, by integrating neural network approximation mechanisms with advanced Nussbaum functions, enabling effective compensation for such nonlinear effects. Building on leader-following consensus protocols and gradient-based game theory, distributed adaptive filtered feedback Nash equilibrium seeking strategies are constructed, with both centralized and decentralized control gains designed accordingly. Finally, a simulation example under different input nonlinearity scenarios is presented to demonstrate the validity of the proposed strategy.

This article investigates the distributed online optimization problem in a zero-sum game between two distinct time-varying multiagent networks. At each iteration, the agents not only communicate with their neighbors but also gather information about agents in the opposing network through a time-varying network, assigning weights accordingly. Moreover, we consider quantized communication and bandit feedback mechanisms, with agents transmitting quantized information and adopting one-point estimators. At each iteration, agents make and submit decisions and then receive the cost function values near their decision points rather than the full cost function information. To guarantee the payoff of each network, we design an algorithm named quantized distributed online bandit optimization in two-network (QDOBO-TN). We use dynamic Nash equilibrium regret to measure the positive payoff discrepancy between the decision sequence produced by Algorithm QDOBO-TN and the Nash equilibrium sequence. Furthermore, we propose a multiepoch version of Algorithm QDOBO-TN. The regret bounds for both algorithms are sublinear with respect to the iteration count T. Finally, we conduct a series of simulation experiments that further validate the effectiveness of the algorithms.

As control systems increasingly rely on limited-bandwidth networks, quantization and data rate constraints present significant challenges for iterative learning control (ILC). This study aims to design a general framework of linear encoding-decoding pairs for quantized ILC under channel transmission constraints. We first develop a unified mathematical framework that integrates existing encoding-decoding schemes within the quantized ILC loop, enabling both the linear encoder and decoder designs to be parameterized by a common set. By employing a p-type controller, we derive a convergence criterion for quantized ILC using the general linear encoding-decoding pair. Furthermore, we introduce a control signal fidelity metric (CSFM) to quantify the discrepancy between the control signal generated with and without a general linear encoding-decoding pair. Based on the CSFM, we provide systematic guidelines for selecting the parameters of the linear encoding-decoding pair. Finally, we establish practical selection rules for the parameters of linear encoding-decoding pairs when finite-level quantizers are used. These rules ensure that no saturation occurs while minimizing both the steady-state output tracking error and the CSFM, thus facilitating the practical quantizer selection in quantized ILC. The theoretical findings are validated through simulations involving industrial robot joint models.

This article investigates reach-avoid games involving defenders equipped with capture radii, where both defenders and attackers have different speeds. The main challenge lies in using geometric methods to analyze different speed ratios, construct barriers, or defensive advantage angles, and divide the state space into defensive and offensive advantage regions. This article proposes optimal analytical strategies for players based on the corresponding payoff functions, depending on the attacker's position within different winning regions under various speed ratios. In addition, we demonstrate the existence of a unique optimal target point within the offensive advantage region. Unlike numerical methods, which are limited by computational complexity and real-time application capabilities, the proposed method allows for the precise calculation of barriers and real-time updates in nonpoint capture scenarios. Finally, simulation results validate the effectiveness of the constructed barriers in multiplayer reach-avoid games.

This article addresses the event-triggered attitude consensus problem for multiple rigid body systems with prescribed-time convergence. Achieving event-triggered prescribed-time attitude consensus almost globally is challenging in the attitude configuration space which is a non-Euclidean manifold. We design an adaptive event-triggered attitude consensus framework by using the exponential coordinates through the logarithm mapping covering$\mathbb {SO}(3)$almost globally. A novel triggering strategy governed by a dynamic variable is proposed to reduce the triggering numbers and guarantee the convergence performance simultaneously. With the proposed adaptive control framework, we achieve almost global attitude consensus with prescribed-time convergence in the event-triggered sampling setting with undirected graphs. Compared to existing results, the proposed adaptive control framework ensures event-triggered prescribed-time attitude consensus in a fully distributed manner, suggesting that the proposed framework does not rely on the global knowledge of the entire topology. Finally, we conduct numerical simulations to validate our results.

This paper proposes three gradient-based neurodynamic optimization approaches for Nash equilibrium seeking in non-cooperative games. The decoupled-gradient and coupled-gradient neurodynamic optimization approaches achieve Nash equilibrium with different fixed-time convergence upper bounds, which are invariant to initial conditions, while the proposed mixed-gradient neurodynamic approach exponentially converges to the Nash equilibrium. The robustness of the proposed fixed-time neurodynamic approaches under vanishing disturbances is also investigated. In addition, three novel analog circuit frameworks are introduced, where the actions of neurons are simulated through a feedback loop composed of multipliers, operational amplifiers, resistors, capacitors, and other basic operation models. The circuits demonstrate that the stable output voltages correspond to the Nash equilibrium. Finally, an example is simulated on Multisim 14.3 to validate the superiority and practicality of the proposed analog circuits.

This study investigates the performance of discrete-time systems under quantized iterative learning control. An encoding-decoding mechanism is combined with a spherical polar coordinate-based quantizer to process the signals transmitted through a control network, which introduces a quantization operation to the encoding process. A scenario involving encoding and decoding of the system output is explored before discussing the general scenario involving encoding and decoding of both the system output and control input. Unlike existing schemes, the two scenarios require no additional scaling parameter in the encoder and decoder. The radius of the support sphere is designed to vary over the iterations, and the learning control scheme is based on the output of the decoder. The results indicate that the control method enables error-free tracking performance of a system. The theoretical conclusions are verified in tests of a permanent magnet synchronous motor.

We focus on the problem of distributed online constrained convex optimization with statistical privacy in multiagent systems. The participating agents aim to collaboratively minimize the cumulative system-wide cost while a passive adversary corrupts some of them. The passive adversary collects information from corrupted agents and attempts to estimate the private information of the uncorrupted ones. In this scenario, we adopt a correlated perturbation mechanism with globally balanced property to cover the local information of agents to enable privacy preservation. This work is the first attempt to integrate such a mechanism into the distributed online (sub)gradient descent algorithm, and then a new algorithm called privacy-preserving distributed online convex optimization (PP-DOCO) is designed. It is proved that the designed algorithm provides a statistical privacy guarantee for uncorrupted agents and achieves an expected regret in $\mathcal {O}(\sqrt {K})$ for convex cost functions, where K denotes the time horizon. Furthermore, an improved expected regret in $\mathcal {O}(\log (K))$ is derived for strongly convex cost functions. The obtained results are equivalent to the best regret scalings achieved by state-of-the-art algorithms. The privacy bound is established to describe the level of statistical privacy using the notion of Kullback-Leibler divergence (KLD). In addition, we observe that a tradeoff exists between our algorithm's expected regret and statistical privacy. Finally, the effectiveness of our algorithm is validated by simulation results.

Finite- and fixed-time parameter estimation and adaptive control have been extensively investigated in recent years. This study proposes a finite- and fixed-time learning control framework to achieve simultaneous finite/fixed-time parameter estimation and control. The proposed learning control method first estimates unknown parameters and then uses these estimates to improve the control performance. Therefore, we first consider the convergence condition of finite/fixed-time parameter estimation. Next, a novel learning-based finite/fixed control law is designed. Unlike most existing adaptation laws, the estimate is updated to improve the understanding of the system rather than eliminate the influence of uncertainties. The finite/fixed-time convergence of the system states is analyzed using a direct dynamic analysis method that differs from the long-used Lyapunov method. We show that the proposed control input satisfies the excitation condition of the finite/fixed-time estimation, indicating simultaneous estimation and control. Finally, numerical simulations are performed to verify the theoretical results.

This article investigates the distributed joint state and fault estimation issue for a class of nonlinear time-varying systems over sensor networks constrained by energy harvesting. It is assumed that data transmission between sensors requires energy consumption, and each sensor can harvest energy from the external environment. A Poisson process models the energy harvested by each sensor, and the sensor's transmission decision depends on its current energy level. One can obtain the sensor transmission probability through a recursive calculation of the probability distribution of the energy level. Under such energy harvesting constraints, the proposed estimator only uses local and neighbor data to simultaneously estimate the system state and the fault, thereby establishing a distributed estimation framework. Moreover, the estimation error covariance is determined to possess an upper bound, which is minimized by devising energy-based filtering parameters. The convergence performance of the proposed estimator is analyzed. Finally, a practical example is presented to verify the usefulness of the main results.

This work studies the security of consensus-based distributed filtering under the replay attack, which can freely select a part of sensors and modify their measurements into previously recorded ones. We analyze the performance degradation of distributed estimation caused by the replay attack, and utilize the Kullback-Leibler (K-L) divergence to quantify the attack stealthiness. Specifically, for a stable system, we prove that under any replay attack, the estimation error is not only bounded, but also can re-enter the steady state. In that case, we prove that the replay attack is ϵ -stealthy, where ϵ can be calculated based on two Lyapunov equations. On the other hand, for an unstable system, we prove that the trace of estimation error covariance is lower bounded by an exponential function, which indicates that the estimation error may diverge due to the attack. In view of this, we provide a sufficient condition to ensure that any replay attack is detectable. Furthermore, we analyze the case that the adversary starts to attack only if the current measurement is close to a previously recorded one. Finally, we verify the theoretical results via several numerical simulations.

This work proposes a design scheme of the desired controller under the lossy digital network by introducing a dynamic coding and packet-length optimization strategy. First, the weighted try once-discard (WTOD) protocol is introduced to schedule the transmission of sensor nodes. The state-dependent dynamic quantizer and the encoding function with time-varying coding length are designed to improve coding accuracy significantly. Then, a feasible state-feedback controller is designed to attain that the controlled system subject to possible packet dropout is exponentially ultimately bounded in the mean-square sense. Moreover, it is shown that the coding error directly affects the convergent upper bound, which is further minimized by optimizing the coding lengths. Finally, the simulation results are provided via the double-sided linear switched reluctance machine systems.

In this article, we consider a distributed constrained optimization problem with delayed subgradient information over the time-varying communication network, where each agent can only communicate with its neighbors and the communication channel has a limited data rate. We propose an adaptive quantization method to address this problem. A mirror descent algorithm with delayed subgradient information is established based on the theory of Bregman divergence. With a non-Euclidean Bregman projection-based scheme, the proposed method essentially generalizes many previous classical Euclidean projection-based distributed algorithms. Through the proposed adaptive quantization method, the optimal value without any quantization error can be obtained. Furthermore, comprehensive analysis on the convergence of the algorithm is carried out and our results show that the optimal convergence rate can be obtained under appropriate conditions. Finally, numerical examples are presented to demonstrate the effectiveness of our results.

This paper investigates the distributed filtering problem for a class of nonlinear systems under edge-based event-triggered (ET) communication. A dynamic edge-based ET mechanism for the sender-receiver ET scheme is proposed. The triggering depends on the relative state information over the edge between the sender and receiver nodes. Compared with the existing synchronous transmission protocols, the sender-receiver ET scheme leads to a more flexible asynchronous communication model by utilizing edge-related triggering parameters. Moreover, this allows the receiver node to be privileged to receive or reject the incoming state information, which is more conducive to reducing the transmission of redundant state information from the sender. If the receiver’s privilege to reject information is not considered, the sender-receiver scheme is further simplified to the sender ET scheme. In the sender ET scheme, the triggering of an edge is only determined by the sender node of the corresponding edge. Both edge-based ET schemes are applied to a unified fully distributed filter design. It is proved that the estimation errors of the proposed distributed filtering algorithm under both schemes are exponentially bounded in the mean square. A simulation example concerning target tracking is given to demonstrate the validity of the main results.

This article investigates the quantized control issue for synchronizing a networked nonlinear system. Due to limited energy and channel resources, the event-triggered control (ETC) method and input quantization are simultaneously taken into account in this article. First, a dynamic quantizer, which discretely adjusts its parameters online and possesses a finite quantization range, is introduced to achieve exact synchronization, rather than quasisynchronization. Next, a new distributed Zeno-free ETC strategy is proposed based on the dynamic quantizer. Then, two different situations, that is, the quantizer is designed with/without the network topology information, are, respectively, discussed. Synchronization criteria are, respectively, derived under such two circumstances by using the Lyapunov method. Finally, numerical examples are provided to show the effectiveness of the theoretical results.

This article is concerned with the distributed stochastic multiagent-constrained optimization problem over a time-varying network with a class of communication noise. This article considers the problem in composite optimization setting, which is more general in the literature of noisy network optimization. It is noteworthy that the mainstream existing methods for noisy network optimization are Euclidean projection based. Based on the Bregman projection-based mirror descent scheme, we present a non-Euclidean method and investigate their convergence behavior. This method is the distributed stochastic composite mirror descent type method (DSCMD-N), which provides a more general algorithm framework. Some new error bounds for DSCMD-N are obtained. To the best of our knowledge, this is the first work to analyze and derive convergence rates of optimization algorithm in noisy network optimization. We also show that an optimal rate of O(1/√T) in nonsmooth convex optimization can be obtained for the proposed method under appropriate communication noise condition. Moveover, novel convergence results are comprehensively derived in expectation convergence, high probability convergence, and almost surely sense.

This article investigates the resilient output synchronization problem of a class of linear heterogeneous multiagent systems subjected to denial-of-service (DoS) attacks. Two types of control mechanisms, namely, event- and self-triggered control mechanisms, are presented so as to cut down unnecessary information transmission. Both of these two mechanisms are distributed, and thus, only local information of each agent and its neighboring agents is adopted for the event condition design. The DoS attacks are considered to be aperiodic, and the quantitative relationship between the attributes of the DoS attacks and the synchronization is also revealed. It is shown that the output synchronization can be achieved exponentially in the presence of DoS attacks under the proposed control mechanisms. The validness of the provided mechanisms is certified by a simulation example.

This article is concerned with the distributed convex constrained optimization over a time-varying multiagent network in the non-Euclidean sense, where the bandwidth limitation of the network is considered. To save the network resources so as to reduce the communication costs, we apply an event-triggered strategy (ETS) in the information interaction of all the agents over the network. Then, an event-triggered distributed stochastic mirror descent (ET-DSMD) algorithm, which utilizes the Bregman divergence as the distance-measuring function, is presented to investigate the multiagent optimization problem subject to a convex constraint set. Moreover, we also analyze the convergence of the developed ET-DSMD algorithm. An upper bound for the convergence result of each agent is established, which is dependent on the trigger threshold. It shows that a sublinear upper bound can be guaranteed if the trigger threshold converges to zero as time goes to infinity. Finally, a distributed logistic regression example is provided to prove the feasibility of the developed ET-DSMD algorithm.

This article investigates the secure consensus problem of general linear multiagent systems with denial-of-service (DoS) attacks. Owning to the existence of DoS attacks, it is challenging to investigate the event-triggered control of multiagent systems in a fully distributed manner. This article presents a novel dynamic event-triggered mechanism to alleviate the limited communication resources. Moreover, the designed mechanism is fully distributed and scalable owing to the introduction of some adaptive coupling weights. Since the DoS attacks have been considered in the event-triggered rule design, a novel adaptive parameter with an additional exponential term is adopted to deal with DoS attacks. The Lyapunov design also introduces such a term for the subsequent stability analysis. Sufficient conditions guaranteeing the asymptotic consensus of the studied system are developed in light of the controller’s parameters, duration, and frequency of the DoS attacks. Strict proof is provided to demonstrate that a secure consensus can be reached effectively under the proposed control mechanism. Furthermore, it is shown that the Zeno behavior can be excluded from the designed triggering mechanism. Finally, simulations on a multiagent system consisting of interconnected unmanned intelligent vehicles are conducted to verify the results.

This article studies the distributed dimensionality reduction fusion estimation problem with communication delays for a class of cyber-physical systems (CPSs). The raw measurements are preprocessed in each sink node to obtain the local optimal estimate (LOE) of a CPS, and the compressed LOE under dimensionality reduction encounters with communication delays during the transmission. Under this case, a mathematical model with compensation strategy is proposed to characterize the dimensionality reduction and communication delays. This model also has the property of reducing the information loss caused by the dimensionality reduction and delays. Based on this model, a recursive distributed Kalman fusion estimator (DKFE) is derived by optimal weighted fusion criterion in the linear minimum variance sense. A stability condition for the DKFE, which can be easily verified by the exiting software, is derived. In addition, this condition can guarantee that the estimation error covariance matrix of the DKFE converges to the unique steady-state matrix for any initial values and, thus, the steady-state DKFE (SDKFE) is given. Note that the computational complexity of the SDKFE is much lower than that of the DKFE. Moreover, a probability selection criterion for determining the dimensionality reduction strategy is also presented to guarantee the stability of the DKFE. Two illustrative examples are given to show the advantage and effectiveness of the proposed methods.

This article is concerned with the model-based event-triggered sliding-mode control (SMC) issue for multi-input systems, which is motivated by some existing results in a single-input case. A model-based event-triggered SMC scheme is first designed. In particular, a triggered condition is co-designed with SMC to achieve the reachability condition of a specified sliding surface. Thus, it can effectively mitigate the burden of data communication, and also eliminate the effect of the matched external disturbance and the model uncertainties in both system and input. For ensuring the stability of the model dynamics and the resulting sliding-mode dynamics simultaneously, an auxiliary disturbance input is introduced to the nominal model by compensating the switching term of the designed SMC law. Furthermore, the positive lower bound for the minimum interevent time is analyzed to ensure the feasibility of the proposed approach. To illustrate the proposed model-based event-triggered SMC approach from a practical viewpoint, two design problems to maximize the system robustness and performance are proposed, respectively. The nontrivial optimization problems are then solved by a genetic algorithm (GA). Finally, jet transport aircraft is utilized to demonstrate the effectiveness of the proposed results and algorithm.

This article studies the distributed linear minimum mean square error (LMMSE) estimation problem for large-scale systems with local information (LSLI). Large-scale systems are composed of numerous subsystems. Each subsystem only transmits information to its neighbors. Thus, only the local information is available to each subsystem. This implies that the information available to different subsystems is different. Using local information to design an LMMSE estimator, the gains of the estimator must satisfy the sparse structure constraint, which makes the estimator design challenging and complicates the boundedness analysis of the estimation error covariance (EEC). In this article, a framework of the distributed LMMSE estimation for LSLI is established. The gains of the LMMSE estimator are effectively constructed by solving linear matrix equations. A gradient descent algorithm is exploited to design the gains of the LMMSE estimator numerically. Sufficient conditions are derived to ensure the boundedness of the EEC. Also, a gradient-based search algorithm is developed to verify whether the sufficient conditions hold or not. Finally, an example is used to illustrate the effectiveness of the proposed results.

This article is concerned with the distributed Kalman filtering problem for interconnected dynamic systems, where the local estimator of each subsystem is designed only by its own information and neighboring information. A decoupling strategy is developed to minimize the impact of interconnected terms on the estimation performance, and then the recursive and distributed Kalman filter is derived in the minimum mean-squared error sense. Moreover, by using Lyapunov criterion for linear time-varying systems, stability conditions are presented such that the designed estimator is bounded. Finally, a heavy duty vehicle platoon system is employed to show the effectiveness and advantages of the proposed methods.

In this article, we study a multiplayer Stackelberg-Nash game (SNG) pertaining to a nonlinear dynamical system, including one leader and multiple followers. At the higher level, the leader makes its decision preferentially with consideration of the reaction functions of all followers, while, at the lower level, each of the followers reacts optimally to the leader's strategy simultaneously by playing a Nash game. First, the optimal strategies for the leader and the followers are derived from down to the top, and these strategies are further shown to constitute the Stackelberg-Nash equilibrium points. Subsequently, to overcome the difficulty in calculating the equilibrium points analytically, we develop a novel two-level value iteration-based integral reinforcement learning (VI-IRL) algorithm that relies only upon partial information of system dynamics. We establish that the proposed method converges asymptotically to the equilibrium strategies under the weak coupling conditions. Moreover, we introduce effective termination criteria to guarantee the admissibility of the policy (strategy) profile obtained from a finite number of iterations of the proposed algorithm. In the implementation of our scheme, we employ neural networks (NNs) to approximate the value functions and invoke the least-squares methods to update the involved weights. Finally, the effectiveness of the developed algorithm is verified by two simulation examples.

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 article considers the problem of stochastic strongly convex optimization over a network of multiple interacting nodes. The optimization is under a global inequality constraint and the restriction that nodes have only access to the stochastic gradients of their objective functions. We propose an efficient distributed non-primal-dual algorithm, by incorporating the inequality constraint into the objective via a smoothing technique. We show that the proposed algorithm achieves an optimal O((1)/(T)) ( T is the total number of iterations) convergence rate in the mean square distance from the optimal solution. In particular, we establish a high probability bound for the proposed algorithm, by showing that with a probability at least 1-δ , the proposed algorithm converges at a rate of O(ln(ln(T)/δ)/ T) . Finally, we provide numerical experiments to demonstrate the efficacy of the proposed algorithm.

Coordination tracking problem of multiagent systems is studied for the application of threat defense in a monitored area. When targets intrude this area, agents which are nearby to them are set to track the targets. Modified nonsingular terminal sliding mode controller is proposed for the agents. We design a novel continuous function in the controller to eliminate the singularity, which makes it able to estimate the finite tracking time. Based on the estimated time, generalized Voronoi diagram considering the velocity of second-order agents and targets is presented. During the tracking process, the event of node failures will trigger a designed coordination strategy. The event that the target enters a new generalized Voronoi cell triggers active replacement coordination strategy. With the proposed active replacement strategy, the tracking time is reduced even under node failures. Comparison lemma is utilized to deal with the agent switching issue caused by node failures or active replacements under new event-triggered coordination strategies.

This paper is concerned with the fixed-time cooperative relay tracking control problem for a set of planar agents in a surveillance network. The plane is partitioned into multiple “capture regions” by using the Voronoi partition according to agents' positions. Once an evader enters into a new capture region, one agent of the tracer team stops and the tracking mission is relayed to another one who is in charge of the new region. As a result, an impulsive model is proposed to describe the problem and a distributed fixed-time cooperative relay control strategy is provided that is not dependent on initial condition. Numerical simulations are provided to demonstrate the validness of the cooperative relay tracking scheme.

This article deals with the observer-based proportional-integral-derivative (PID) security control problem for a kind of linear discrete time-delay systems subject to cyber-attacks. The cyber-attacks, which include both denial-of-service and deception attacks, are allowed to be randomly occurring as regulated by two sequences of Bernoulli distributed random variables with certain probabilities. A novel observer-based PID controller is proposed such that the closed-loop system achieves the desired security level and the quadratic cost criterion (QCC) has an upper bound. Sufficient conditions are derived under which the exponentially mean-square input-to-state stability is guaranteed and the desired security level is then achieved. Subsequently, an upper bound of the QCC is obtained and the explicit expression of the desired PID controller is also parameterized. Finally, the validity of the developed design approach is verified via an illustrative example.

In this paper, the partial-nodes-based state estimators (PNBSEs) are designed for a class of uncertain complex networks subject to finite-distributed delays, stochastic disturbances, as well as randomly occurring deception attacks (RODAs). In consideration of the likely unavailability of the output signals in harsh environments from certain network nodes, only partial measurements are utilized to accomplish the state estimation task for the addressed complex network with norm-bounded uncertainties in both the network parameters and the inner couplings. The RODAs are taken into account to reflect the compromised data transmissions in cyber security. We aim to derive the gain parameters of the estimators such that the overall estimation error dynamics satisfies the specified security constraint in the simultaneous presence of stochastic disturbances and deception signals. Through intensive stochastic analysis, sufficient conditions are obtained to guarantee the desired security performance for the PNBSEs, based on which the estimator gains are acquired by solving certain matrix inequalities with nonlinear constraints. A simulation study is carried out to testify the security performance of the presented state estimation method.

Impulsive control of nonlinear delay systems is studied in this paper, where the time delays addressed may be the constant delay, bounded time-varying delay, or unbounded time-varying delay. Based on the impulsive control theory and some analysis techniques, a new theoretical result for global exponential stability is derived from the impulsive control point of view. The significance of the presented result is that the stability can be achieved via the impulsive control at certain impulse points despite the existence of impulsive perturbations which causes negative effect to the control. That is, the impulsive control provides a super performance to allow the existence of impulsive perturbations. In addition, we apply the theoretical result to the problem of impulsive control of delayed neural networks. Some results for global exponential stability and synchronization control of neural networks with time delays are derived via impulsive control. Three illustrated examples are given to show the effectiveness and distinctiveness of the proposed impulsive control schemes.

Most existing finite-/fixed-time synchronization control schemes are nonsmooth or discontinuous, and the settling time is estimated with conservatism. It is due to the utilization of signum function or fraction power state feedback. This brief considers the problem of prespecified-time cluster synchronization of complex networks with a smooth control protocol. The synchronization time is independent of any control parameters or any systems' initial conditions, which is actually uniformly prescribed according to task requirements without any estimations. Moreover, the cluster synchronization can maintain after the specified time, and the smooth control input can always keep uniformly bounded in an infinite time interval as well. Finally, one numerical example is provided to illustrate the effectiveness of the proposed protocol and design method.

The tracking for discrete systems is discussed by designing two kinds of multilayered iterative learning schemes with cooperative-antagonistic interactions in this paper. The definition of the signed graph is presented and iterative learning schemes are then designed to be multilayered and have cooperative-antagonistic interactions. Moreover, considering the limited bandwidth of information storage, the state information of these controllers is updated in light of previous learning iterations but not just dependent on the last iteration. Two simple criteria are addressed to discuss the tracking of discrete systems with multilayered and cooperative-antagonistic iterative schemes. The simulation results are shown to demonstrate the validity of the given criteria.

This paper develops a fully distributed framework to investigate the cooperative behavior of multiagent systems in the presence of distributed denial-of-service (DoS) attacks launched by multiple adversaries. In such an insecure network environment, two kinds of communication schemes, that is, sample-data and event-triggered communication schemes, are discussed. Then, a fully distributed control protocol with strong robustness and high scalability is well designed. This protocol guarantees asymptotic consensus against distributed DoS attacks. In this paper, "fully" emphasizes that the eigenvalue information of the Laplacian matrix is not required in the design of both the control protocol and event conditions. For the event-triggered case, two effective dynamical event-triggered schemes are proposed, which are independent of any global information. Such event-triggered schemes do not exhibit Zeno behavior even in the insecure environment. Finally, a simulation example is provided to verify the effectiveness of theoretical analysis.

The resilient control refers to the control methodology which provides an interdisciplinary solution to secure the control system. In this paper, the resilient control problem is investigated for a class of wireless networked control systems (WNCS) under a denial-of-service (DoS) attack. In the presence of the DoS attacker, the control command sent by the transmitter may be interfered, which can cause the degradation of the signal-to-interference-plus-noise ratio and further lead to packet dropout phenomenon. Such a packet dropout phenomenon is described by a two-state Markov-chain. A cross-layer view is adopted toward the security issue of the considered WNCS. The Nash power strategies and optimal control strategy in the delta-domain are obtained in the cyber- and physical-layer, respectively. Based on the obtained strategies, the coupled-design problem is solved which aims to drive the underlying control performance to the desired security region by dynamically manipulating the cyber-layer pricing parameters. Finally, a numerical simulation is conducted to verify the validity of the proposed methodology.

In this paper, the quasi-consensus problem is investigated for a class of heterogeneous-switched nonlinear multiagent systems, in which both cooperation and competition interactions are considered simultaneously. By means of the Lyapunov function method, we show that quasi-consensus can be ensured for switched multiagent systems under the assumption that the activation time of cooperation interactions is sufficiently large. Moreover, a new Lyapunov function is considered to provide the lower and upper bounds of switching intervals explicitly. Thus, these bounds can be used to obtain less conservative stability results of switched systems. Furthermore, the established results are specialized to both the traditional consensus case and the stability of linear-switched systems. Finally, simulations are given to illustrate the theoretical results derived in this paper.

In this paper, the leader-following consensus problem of multiagent systems with general dynamics under event-triggered mechanisms is investigated. A centralized event-triggered mechanism (CEM) is first proposed. Then, a distributed dynamic event-triggered mechanism is developed by introducing an internal variable. In the CEM case, each agent uses global information of the multiagent system, while in the distributed case, each agent only uses local information of its own and its neighbors. The multiagent system can achieve asymptotic consensus as well as exclude the Zeno phenomenon under the designed event-triggered rules in both cases. A multiagent system consisting of interconnected pendulums is provided to demonstrate the merits and correctness of the proposed methods.

In the presence of malicious denial-of-service (DoS) attacks, this paper investigates the tracking control of mobile robots. Some explicit characterizations are presented for frequency and duration properties of malicious DoS attacks. A hybrid model is established by considering malicious DoS attacks and event-triggering control. The significance of this paper is to develop a set of event-triggering conditions to ensure the tracking convergence. As well, these conditions can guarantee the existence of uniformly positively minimum interval between any two successive transmissions. Finally, a practical experiment is presented by considering the tracking control of an Amigobot mobile robot over a wireless network with DoS attacks, which verifies the effectiveness of the derived results.

This brief proposes a unified theoretical framework to investigate the finite/fixed-time synchronization of complex networks with stochastic disturbances. By designing a common pinning controller with different ranges of power parameters, both the goals of finite-time and fixed-time synchronization in probability for the network topology containing spanning trees can be achieved. Moveover, with the help of finite-time stochastic stability theory, two types of explicit expressions of finite/fixed (dependent/independent on the initial values) settling times are calculated as well. One numerical example is finally presented to demonstrate the effectiveness of the theoretical analysis.

Due to properties of flexibility, adaptiveness, error tolerance, and time-determinism performance, the FlexRay communication protocol has been widely used to investigate robot systems and new generation of automobiles. In this paper, with the FlexRay communication protocol, the tracking problem of a class of cyber-physical systems are investigated by developing a general hybrid model, in which an emulation controller is utilized. Based on the proposed hybrid model, some sufficient conditions are established to guarantee the convergence of tracking errors. Then, the maximum allowable transmission interval (MATI) of the static/dynamic segment is obtained with a more general formula than the ones in some the previous works. The obtained MATI over the FlexRay communication network can be adjusted via the appropriate length of the static/dynamic segment, which reflects the flexibility of FlexRay. Finally, the results are verified by considering the tracking problem of a single-link robot arm system as well as the stabilization of a batch reactor system.

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.

This paper investigates the leader-following consensus issue with event/self-triggered schemes under an unreliable network environment. First, we characterize network communication and control protocol update in the presence of denial-of-service (DoS) attacks. In this situation, an event-triggered communication scheme is first proposed to effectively schedule information transmission over the network possibly subject to malicious attacks. In this communication framework, synchronous and asynchronous updated strategies of control protocols are constructed to achieve leader-following consensus in the presence of DoS attacks. Moreover, to further reduce the cost induced by event detection, a self-triggered communication scheme is proposed in which the next triggering instant can be determined by computing with the most updated information. Finally, a numerical example is provided to verify the effectiveness of the proposed communication schemes and updated strategies in the unreliable network environment.

This paper studies the distributed dimensionality reduction fusion estimation problem for a class of cyber-physical systems (CPSs) under denial-of-service (DoS) attacks. The problem is modeled under the resource constraints (i.e., bandwidth or energy) for the defender and attacker. Based on a new attack and compensation model, a recursive distributed Kalman fusion estimator (DKFE) is designed for the addressed CPSs. Though the optimization objects of the defender and attacker are opposite, the corresponding optimization problems are established based on different available information. In this case, an explicit form of suboptimal dimensionality reduction is given against DoS attacks, while an effective attack strategy is proposed for the attacker. A stability condition is derived such that the mean square error of the designed DKFE is bounded. Two illustrative examples are given to show the effectiveness of the proposed methods.

State estimation plays an essential role in the monitoring and supervision of cyber-physical systems (CPSs), and its importance has made the security and estimation performance a major concern. In this case, multisensor information fusion estimation (MIFE) provides an attractive alternative to study secure estimation problems because MIFE can potentially improve estimation accuracy and enhance reliability and robustness against attacks. From the perspective of the defender, the secure distributed Kalman fusion estimation problem is investigated in this paper for a class of CPSs under replay attacks, where each local estimate obtained by the sink node is transmitted to a remote fusion center through bandwidth constrained communication channels. A new mathematical model with compensation strategy is proposed to characterize the replay attacks and bandwidth constrains, and then a recursive distributed Kalman fusion estimator (DKFE) is designed in the linear minimum variance sense. According to different communication frameworks, two classes of data compression and compensation algorithms are developed such that the DKFEs can achieve the desired performance. Several attack-dependent and bandwidth-dependent conditions are derived such that the DKFEs are secure under replay attacks. An illustrative example is given to demonstrate the effectiveness of the proposed methods.

This paper is concerned with the finite-horizon consensus problem for a class of discrete time-varying multiagent systems with external disturbances and missing measurements. To improve the communication reliability, redundant channels are introduced and the corresponding protocol is constructed for the information transmission over redundant channels. An event-triggered scheme is adopted to determine whether the information of agents should be transmitted to their neighbors. Subsequently, an observer-type event-triggered control protocol is proposed based on the latest received neighbors' information. The purpose of the addressed problem is to design a time-varying controller based on the observed information to achieve the consensus performance in a finite horizon. By utilizing a constrained recursive Riccati difference equation approach, some sufficient conditions are obtained to guarantee the consensus performance, and the controller parameters are also designed. Finally, a numerical example is provided to demonstrate the desired reliability of redundant channels and the effectiveness of the event-triggered control protocol.

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.

By designing synchronous and asynchronous iterative learning controllers, the tracking problem of Takagi-Sugeno (T-S) fuzzy systems with measurable and unmeasurable state information is investigated in this paper. The T-S fuzzy model is first constructed to describe dynamic systems with a variable structure. Iterative learning controllers are then designed to achieve the tracking problem of T-S fuzzy systems. Here, the iterative learning controllers are designed to be synchronous and asynchronous. Also, system states are considered to be measurable and unmeasurable due to the capability of transmission bandwidth of networks and external and/or internal disturbances. Finally, simulation results are given to illustrate the usefulness of the developed criteria.

In this brief, we study the detectability issues in the context of distributed state estimation problems for a class of locally undetectable sensor networks. First, we introduce a novel detectability condition, i.e., weightedly uniform detectability (WUD), which is a sufficient condition to prove that the error covariances of the consensus filtering are uniformly bounded even though the local sensor nodes are undetectable. Different from the existing detectability (or observability) conditions, our condition includes the interacting weights which could further optimize the lower detectability Gramian bound. Hence, a new weights selection method is derived in term of the criterion of WUD. This new rule of selecting weights provides a new framework for distributed state estimation. The advantages of this approach lead to a better performance in estimation without extra computational burden to the filtering process. Finally, an example shows the effectiveness of the proposed method.

This paper proposes two second-order continuous-time algorithms to solve the economic power dispatch problem in smart grids. The collective aim is to minimize a sum of generation cost function subject to the power demand and individual generator constraints. First, in the framework of nonsmooth analysis and algebraic graph theory, one distributed second-order algorithm is developed and guaranteed to find an optimal solution. As a result, the power demand constraints can be kept all the time under appropriate initial condition. The second algorithm is under a centralized framework, and the optimal solution is robust in the sense that different initial power conditions do not change the convergence of the optimal solution. Finally, simulation results based on five-unit system, IEEE 30-bus system, and IEEE 300-bus system show the effectiveness and performance of the proposed continuous-time algorithms. The examples also show that the convergence rate of second-order algorithm is faster than that of first-order distributed algorithm.

This paper is concerned with the semi-global output synchronization problem of a heterogeneous network under event-triggered control mechanism. A distributed event-triggered scheme is proposed in this paper. The Zeno behavior can also be excluded in the designed scheme. By adopting the low-gain technique, it is shown that the input saturation nonlinearity can be avoided if the parameter of the parameterized feedback gain is chosen small enough. A simulation example is provided to validate the effectiveness of the proposed scheme.

In this paper, the observer-based event-triggering consensus control problem is investigated for a class of discrete-time multiagent systems with lossy sensors and cyber-attacks. A novel distributed observer is proposed to estimate the relative full states and the estimated states are then used in the feedback protocol in order to achieve the overall consensus. An event-triggered mechanism with state-independent threshold is adopted to update the control input signals so as to reduce unnecessary data communications. The success ratio of the launched attacks is taken into account to reflect the probabilistic failures of the attacks passing through the protection devices subject to limited resources and network fluctuations. The purpose of the address problem is to design an observer-based distributed controller such that the closed-loop multiagent system achieves the prescribed consensus in spite of the lossy sensors and cyber-attacks. By making use of eigenvalues and eigenvectors of the Laplacian matrix, the closed-loop system is transformed into an easy-to-analyze setting and then a sufficient condition is derived to guarantee the desired consensus. Furthermore, the controller gain is obtained in terms of the solution to certain matrix inequality which is independent of the number of agents. An algorithm is provided to optimize the consensus bound. Finally, a simulation example is utilized to illustrate the usefulness of the proposed controller design scheme.

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

This paper investigates the leader-following consensus for multiagent systems with general linear dynamics by means of event-triggered scheme (ETS). We propose three types of schemes, namely, distributed ETS (distributed-ETS), centralized ETS (centralized-ETS), and clustered ETS (clustered-ETS) for different network topologies. All these schemes guarantee that all followers can track the leader eventually. It should be emphasized that all event-triggered protocols in this paper depend on local information and their executions are distributed. Moreover, it is shown that such event-triggered mechanism can significantly reduce the frequency of control's update. Further, positive inner-event time intervals are assured for those cases of distributed-ETS, centralized-ETS, and clustered-ETS. In addition, two methods are proposed to avoid continuous communication between agents for event detection. Finally, numerical examples are provided to illustrate the effectiveness of the ETSs.

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.

This issue marks the first anniversary issue since I was honored to serve as the Editor-in-Chief (EiC) of the IEEE Transactions on Neural Networks and Learning Systems (TNNLS). I am happy to report that we had a very successful year and here are a few highlights that I would like to share with the community.•The latest impact factor of TNNLS is 4.854 according to the Journal Citation Reports. This marks a record high impact factor for our journal and places TNNLS as the number one scholarly publication in Computer Science (Hardware & Architecture), number three in Computer Science (Theory & Methods), and number ten in Electrical and Electronic Engineering journals.

This brief investigates the problem of finite-time robust consensus (FTRC) for second-order nonlinear multiagent systems with external disturbances. Based on the global finite-time stability theory of discontinuous homogeneous systems, a novel finite-time convergent discontinuous disturbed observer (DDO) is proposed for the leader-following multiagent systems. The states of the designed DDO are then used to design the control inputs to achieve the FTRC of nonlinear multiagent systems in the presence of bounded disturbances. The simulation results are provided to validate the effectiveness of these theoretical results.

This paper studies the distributed robust fusion estimation problem with stochastic and deterministic parameter uncertainties, where the covariance of the Gaussian white noise is unknown, and the covariances of the random variables in the stochastic uncertainties are in a bounded set. By using the discrete-time stochastic bounded real lemma and the matrix analysis approach, each local robust estimator is derived to guarantee an optimal estimation performance for admissible uncertainties, and then necessary and sufficient condition for the distributed robust fusion estimator is presented to obtain an optimal weighting fusion criterion. Note that the local robust estimation problem and the distributed robust fusion estimation problem are both converted into convex optimization problems, which can be easily solved by standard software packages. The advantage and effectiveness of the proposed methods are demonstrated through state monitoring for target tracking system and stirred rank reactor system.

This paper proposes a new event-triggered scheme, in which each agent has various mechanisms to respectively determine when to exchange information with each of its different neighbors. This kind of event-triggered mechanism avoids two constraints in previous mechanisms: (1) simultaneous event detection; (2) synchronous information transmission to all of neighbors. Thus our proposed scheme can be applied into more general situations. In addition, our scheme is able to guarantee the asymptotic consensus and exclude the Zeno behavior. Furthermore, an alternative self-triggered algorithm is presented to thoroughly exclude continuous event detection. Finally, a numerical example is provided to verify the theoretical analysis.

This paper considers the asymptotic and finite-time synchronization of drive-response memristive neural networks (MNNs) with time-varying delays. It is known that the parameters of MNNs are state-dependent, and hence the traditional robust control and analytical techniques cannot be directly applied. This difficulty is overcome by using the concept of Filippov solution. However, the special characteristics of MNNs may lead to unexpected parameter mismatch issue when different initial conditions are chosen. Based on a new robust control design, the mismatching issue is solved. Sufficient conditions are derived to guarantee the asymptotic synchronization of the considered MNNs with delays, which may be less conservative than synchronization criterion obtained by using existing methods. Moreover, without using the existing finite-time stability theorem, finite-time synchronization of the MNNs with delays is also investigated. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical analysis.

In this paper, we study the distributed constrained optimization problem where the objective function is the sum of local convex cost functions of distributed nodes in a network, subject to a global inequality constraint. To solve this problem, we propose a consensus-based distributed regularized primal-dual subgradient method. In contrast to the existing methods, most of which require projecting the estimates onto the constraint set at every iteration, only one projection at the last iteration is needed for our proposed method. We establish the convergence of the method by showing that it achieves an O ( K (-1/4) ) convergence rate for general distributed constrained optimization, where K is the iteration counter. Finally, a numerical example is provided to validate the convergence of the propose method.

Multiagent systems (MASs) are ubiquitous in our real world. There is an increasing attention focusing on the consensus (or synchronization) problem of MASs over the past decade. Although there are numerous results reported on the convergence of a discrete-time MAS based on the infinite products of matrices, few results are on the convergence rate. Because of the switching topology, the traditional eigenvalue analysis and the Lyapunov function methods are both invalid for the convergence rate analysis of an MAS with a switching topology. Therefore, the estimation of the convergence rate for a discrete-time MAS with time-varying delays remains a difficult problem. To overcome the essential difficulty of switching topology, this paper aims at developing a contractive-set approach to analyze the convergence rate of a discrete-time MAS in the presence of time-varying delays and generalized coupling coefficients. Using the proposed approach, we obtain an upper bound of the convergence rate under the condition of joint connectivity. In particular, the proposed method neither requires the nonnegative property of the coupling coefficients nor the basic assumption of a uniform lower bound for all positive coupling coefficients, which have been widely applied in the existing works on this topic. As an application of the main results, we will show that the classical Vicsek model with time delays can realize synchronization if the initial topology is connected.

This brief investigates the interval iterative learning problem for dynamic systems with hierarchical neural network (HNN)-structural output. The first objective is to design the output of a dynamic system with HNN structure. A sufficient condition is obtained to achieve the interval tracking in a finite interval by applying iterative learning control (ILC). Then, the saturated ILC is considered into the discussed system, and a less conservative criterion is obtained to achieve the tracking in a finite interval using a network structure decomposition technique. Finally, simulation results are given to illustrate the usefulness of the developed criteria.

This paper studies the problem of minimizing a sum of (possible nonsmooth) convex functions that are corresponding to multiple interacting nodes, subject to a convex state constraint set. Time-varying directed network is considered here. Two types of computational constraints are investigated in this paper: one where the information of gradients is not available and the other where the projection steps can only be calculated approximately. We devise a distributed zeroth-order method, the implementation of which needs only functional evaluations and approximate projection. In particular, we show that the proposed method generates expected function value sequences that converge to the optimal value, provided that the projection errors decrease at appropriate rates.

In this paper, fault-tolerant consensus in multi-agent system using distributed adaptive protocol is investigated. Firstly, distributed adaptive online updating strategies for some parameters are proposed based on local information of the network structure. Then, under the online updating parameters, a distributed adaptive protocol is developed to compensate the fault effects and the uncertainty effects in the leaderless multi-agent system. Based on the local state information of neighboring agents, a distributed updating protocol gain is developed which leads to a fully distributed continuous adaptive fault-tolerant consensus protocol design for the leaderless multi-agent system. Furthermore, a distributed fault-tolerant leader-follower consensus protocol for multi-agent system is constructed by the proposed adaptive method. Finally, a simulation example is given to illustrate the effectiveness of the theoretical analysis.

This paper studies the stability and Hopf bifurcation in a class of high-dimension neural network involving the discrete and distributed delays under a new framework. By introducing some virtual neurons to the original system, the impact of distributed delay can be described in a simplified way via an equivalent new model. This paper extends the existing works on neural networks to high-dimension cases, which is much closer to complex and real neural networks. Here, we first analyze the Hopf bifurcation in this special class of high dimensional model with weak delay kernel from two aspects: one is induced by the time delay, the other is induced by a rate parameter, to reveal the roles of discrete and distributed delays on stability and bifurcation. Sufficient conditions for keeping the original system to be stable, and undergoing the Hopf bifurcation are obtained. Besides, this new framework can also apply to deal with the case of the strong delay kernel and corresponding analysis for different dynamical behaviors is provided. Finally, the simulation results are presented to justify the validity of our theoretical analysis.

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.

In this brief, we consider the multiagent optimization over a network where multiple agents try to minimize a sum of nonsmooth but Lipschitz continuous functions, subject to a convex state constraint set. The underlying network topology is modeled as time varying. We propose a randomized derivative-free method, where in each update, the random gradient-free oracles are utilized instead of the subgradients (SGs). In contrast to the existing work, we do not require that agents are able to compute the SGs of their objective functions. We establish the convergence of the method to an approximate solution of the multiagent optimization problem within the error level depending on the smoothing parameter and the Lipschitz constant of each agent's objective function. Finally, a numerical example is provided to demonstrate the effectiveness of the method.

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.

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.

In this paper, the consensus problem of multiagent nonlinear directed networks (MNDNs) is discussed in the case that a MNDN does not have a spanning tree to reach the consensus of all nodes. By using the Lie algebra theory, a linear node-and-node pinning method is proposed to achieve a consensus of a MNDN for all nonlinear functions satisfying a given set of conditions. Based on some optimal algorithms, large-size networks are aggregated to small-size ones. Then, by applying the principle minor theory to the small-size networks, a sufficient condition is given to reduce the number of controlled nodes. Finally, simulation results are given to illustrate the effectiveness of the developed criteria.

In this paper, the robustH∞-control problem is investigated for a class of uncertain discrete-time fuzzy systems with both multiple probabilistic delays and multiple missing measurements. A sequence of random variables, all of which are mutually independent but obey the Bernoulli distribution, is introduced to account for the probabilistic communication delays. The measurement-missing phenomenon occurs in a random way. The missing probability for each sensor satisfies a certain probabilistic distribution in the interval. Here, the attention is focused on the analysis and design ofH∞fuzzy output-feedback controllers such that the closed-loop Takagi-Sugeno (T-S) fuzzy-control system is exponentially stable in the mean square. The disturbance-rejection attenuation is constrained to a given level by means of theH∞-performance index. Intensive analysis is carried out to obtain sufficient conditions for the existence of admissible output feedback controllers, which ensures the exponential stability as well as the prescribedH∞performance. The cone-complementarity-linearization procedure is employed to cast the controller-design problem into a sequential minimization one that is solved by the semi-definite program method. Simulation results are utilized to demonstrate the effectiveness of the proposed design technique in this paper.

This paper deals with the filtering problem for discrete-time fuzzy stochastic systems with sensor nonlinearities. There exist time-varying parameter uncertainties and random noise depending on state and external-disturbance. The characteristic of nonlinear sensor is handled by a decomposition method. By means of the parallel distributed compensation technique, the design method of the robust H_ filter is presented. Sufficient conditions for the stochastic stability of the filtering error systems are derived such that the filter parameters can be explicitly obtained. Simulation results are given to illustrate the proposed method.

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.

The paper deals with the robust fault detection problem for Takagi–Sugeno (T--S) fuzzy ItÔ stochastic systems. Our aim is to develop a robust fault detection approach to the T--S fuzzy systems with Brownian motion. By using a general observer-based fault detection filter as a residual generator, the robust fault detection is formulated as a filtering problem. Attention is focused on the design of both the fuzzy-rule-independent and the fuzzy-rule-dependent fault detection filters guaranteeing a prescribed noise attenuation level in an${{\H}}_\infty$sense. Sufficient conditions are proposed to guarantee the mean-square asymptotic stability with an${{\H}}_\infty$performance for the fault detection system. The corresponding solvability conditions for the desired fuzzy-rule-independent and fuzzy-rule-dependent fault detection filters are also established. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory.

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.

For original paper see D. W. C. Ho et al., ibid., vol.16, no.3, p.625-35, (2005). For original paper see S. J. Yoo et al., ibid., vol.19, no.8, p.1496-8, (2008). This paper presents the reply to "Comments on ldquoAdaptive neural control for a class of nonlinearly parametric time-delay systemsrdquordquo.

This paper deals with the sliding-mode control (SMC) problem for nonlinear stochastic time-delay systems by means of fuzzy approach. The Takagi-Sugeno (T-S) fuzzy stochastic time-delay model with parametric uncertainties and unknown nonlinearities is presented. A sufficient condition for the exponential stability in mean square of the sliding motion is also derived. Moreover, it is shown that when the linear matrix inequalities (LMIs) with equality constraint are feasible, the designs of both sliding surface and sliding-mode controller can be easily obtained via convex optimization. A simulation example illustrating the proposed method is given.

The Takagi-Sugeno (T-S) model of fuzzy delay systems with impulse is first presented in this paper. By means of classical analysis methods and Razumikhin technique, the criteria of uniform stability and uniform asymptotic stability for T-S fuzzy delay systems with impulse are obtained, respectively. Three numerical examples are also discussed to illustrate the efficiency of the obtained results.

In this paper, the robust H infinity control problem is considered for a class of networked systems with random communication packet losses. Because of the limited bandwidth of the channels, such random packet losses could occur, simultaneously, in the communication channels from the sensor to the controller and from the controller to the actuator. The random packet loss is assumed to obey the Bernoulli random binary distribution, and the parameter uncertainties are norm-bounded and enter into both the system and output matrices. In the presence of random packet losses, an observer-based feedback controller is designed to robustly exponentially stabilize the networked system in the sense of mean square and also achieve the prescribed H infinity disturbance-rejection-attenuation level. Both the stability-analysis and controller-synthesis problems are thoroughly investigated. It is shown that the controller-design problem under consideration is solvable if certain linear matrix inequalities (LMIs) are feasible. A simulation example is exploited to demonstrate the effectiveness of the proposed LMI approach.

Global asymptotic stabilization for a class of delayed bilinear descriptor systems is first studied in this paper. New approaches are developed by means of the LaSalle invariant principle for delayed nonlinear systems. A new set of sufficient condition is first derived via the continuous static state feedback, the feedback not only guarantees the existence and uniqueness of solution but also the global asymptotical stabilization for the closed loop system

In this letter, we consider the robust finite-horizon filtering problem for a class of discrete time-varying systems with missing measurements and norm-bounded parameter uncertainties. The missing measurements are described by a binary switching sequence satisfying a conditional probability distribution. An upper bound for the state estimation error variance is first derived for all possible missing observations and all admissible parameter uncertainties. Then, a robust filter is designed, guaranteeing that the variance of the state estimation error is not more than the prescribed upper bound. It is shown that the desired filter can be obtained in terms of the solutions to two discrete Riccati difference equations, which are of a form suitable for recursive computation in online applications. A simulation example is presented to show the effectiveness of the proposed approach by comparing to the traditional Kalman filtering method.

In this paper, an adaptive neural controller for a class of time-delay nonlinear systems with unknown nonlinearities is proposed. Based on a wavelet neural network (WNN) online approximation model, a state feedback adaptive controller is obtained by constructing a novel integral-type Lyapunov-Krasovskii functional, which also efficiently overcomes the controller singularity problem. It is shown that the proposed method guarantees the semiglobal boundedness of all signals in the adaptive closed-loop systems. An example is provided to illustrate the application of the approach.

In this letter, the state estimation problem is studied for neural networks with time-varying delays. The interconnection matrix and the activation functions are assumed to be norm-bounded. The problem addressed is to estimate the neuron states, through available output measurements, such that for all admissible time-delays, the dynamics of the estimation error is globally exponentially stable. An effective linear matrix inequality approach is developed to solve the neuron state estimation problem. In particular, we derive the conditions for the existence of the desired estimators for the delayed neural networks. We also parameterize the explicit expression of the set of desired estimators in terms of linear matrix inequalities (LMIs). Finally, it is shown that the main results can be easily extended to cope with the traditional stability analysis problem for delayed neural networks. Numerical examples are included to illustrate the applicability of the proposed design method.

This paper considers the problem of robust exponential epsilon-regulation for a class of multi-input nonlinear systems with uncertainties. The uncertainties appear not only in the feedback channel but also in the control channel. Under some mild assumptions, an adaptive neural network control scheme is developed such that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded and, under the control scheme with initial data starting in some compact set, the states of the closed-loop system is guaranteed to exponentially converge to an arbitrarily specified epsilon-neighborhood about the origin. The important contributions of the present work are that a new exponential uniformly ultimately bounded performance is proposed and that the design parameters and initial condition set can be determined easily. The development generalizes and improves earlier results for the single-input case.

In this paper, we are concerned with a new control problem for uncertain discrete-time stochastic systems with missing measurements. The parameter uncertainties are allowed to be norm-bounded and enter into the state matrix. The system measurements may be unavailable (i.e., missing data) at any sample time, and the probability of the occurrence of missing data is assumed to be known. The purpose of this problem is to design an output feedback controller such that, for all admissible parameter uncertainties and all possible incomplete observations, the system state of the closed-loop system is mean square bounded, and the steady-state variance of each state is not more than the individual prescribed upper bound. We show that the addressed problem can be solved by means of algebraic matrix inequalities. The explicit expression of the desired robust controllers is derived in terms of some free parameters, which may be exploited to achieve further performance requirements. An illustrative numerical example is provided to demonstrate the usefulness and flexibility of the proposed design approach.

This paper considers the problem of global robust stability analysis of delayed cellular neural networks (DCNNs) with norm-bounded parameter uncertainties. In terms of a linear matrix inequality, a new sufficient condition ensuring a nominal DCNN to have a unique equilibrium point which is globally asymptotically stable is proposed. This condition is shown to be a generalization and improvement over some previous criteria. Based on the stability result, a robust stability condition is developed, which contains an existing robust stability result as a special case. An example is provided to demonstrate the reduced conservativeness of the proposed results.

This paper addresses the problem of the robust stabilization and the state estimation (RSSE) for uncertain stochastic discrete-delay large-scale systems. The purpose of this problem is to design a decentralized output feedback controller based on local observers such that, for all admissible parameter uncertainties, the resulting closed-loop system is robustly stochastically stable. A sufficient condition for solving the above problem is obtained by means of linear matrix inequality (LMI) techniques. A numerical example is provided to demonstrate the effectiveness of the proposed design approach.

Takagi-Sugeno (T-S) fuzzy models are now often used to describe complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear submodels. In this note, the T-S fuzzy model approach is exploited to establish stability criteria for a class of nonlinear stochastic systems with time delay. Sufficient conditions are derived in the format of linear matrix inequalities (LMIs), such that for all admissible parameter uncertainties, the overall fuzzy system is stochastically exponentially stable in the mean square, independent of the time delay. Therefore, with the numerically attractive Matlab LMI toolbox, the robust stability of the uncertain stochastic fuzzy systems with time delays can be easily checked.

Inspired by the theory of multiresolution analysis (MRA) of wavelet transforms and fuzzy concepts, a fuzzy wavelet network (FWN) is proposed for approximating arbitrary nonlinear functions. The FWN consists of a set of fuzzy rules. Each rule corresponding to a sub-wavelet neural network (WNN) consists of single-scaling wavelets. Through efficient bases selection, the dimension of the approximated function does not cause the bottleneck for constructing FWN. Especially, by learning the translation parameters of the wavelets and adjusting the shape of membership functions, the model accuracy and the generalization capability of the FWN can be remarkably improved. Furthermore, an algorithm for constructing and training the fuzzy wavelet networks is proposed. Simulation examples are also given to illustrate the effectiveness of the method.