Event-Triggered Multiasynchronous H∞ Control for Markov Jump Systems With Transmission Delay.

In this article, the issue of event-triggered multiasynchronous H∞ control for Markov jump systems with transmission delay is concerned. In order to reduce sampling frequency, multiple event-triggered schemes (ETSs) are introduced. Then hidden Markov model (HMM) is employed to describe multiasynchronous jumps among subsystems, ETSs, and controller. Based on the HMM, the time-delay closed-loop model is constructed. In particular, when triggered data are transmitted over networks, a large transmission delay may cause disorder of transmission data such that the time-delay closed-loop model cannot be developed directly. To overcome this difficulty, a packet loss schedule is presented and the unified time-delay closed-loop system is obtained. By the use of the Lyapunov-Krasovskii functional method, sufficient conditions with the controller design are formulated for guaranteeing the H∞ performance of the time-delay closed-loop system. Finally, the effectiveness of the proposed control strategy is demonstrated by two numerical examples.

H∞ Controller Design for Networked Systems With Two-Channel Packet Dropouts and FDI Attacks.

In this article, the stochastic analysis and H∞ controller design problems of networked systems with packet dropouts and false data injection attacks are investigated. Different from the existing literature, we focus on the linear networked systems with external disturbances and both sensor-controller channel and controller-actuator channel are studied. First, we present a discrete-time modeling framework that leads to a stochastic closed-loop system with randomly varying parameters. To facilitate the analysis and H∞ control of resulting discrete-time stochastic closed-loop system, an equivalent yet analyzable stochastic augmented model is further constructed by matrix exponential computation. Based on this model, a stability condition is derived in the form of linear matrix inequality (LMI) with the aid of a reduced-order confluent Vandermonde matrix, Kronecker product operation, and law of total expectation. Specifically, the dimension of the LMI obtained in this article does not increase as the upper bound of consecutive packet dropouts does, which is also different from the existing literature. Subsequently, a desired H∞ controller is obtained such that the original discrete-time stochastic closed-loop system is exponentially mean-square stable with a prescribed H∞ performance. Finally, a numerical example and a direct current motor system are exploited to substantiate the effectiveness and practicability of the designed strategy.

Stability and Stabilization of Nonlinear Stochastic Systems With Synchronous and Asynchronous Switching Parameters to the States.

This article is concerned with the stability and stabilization of nonlinear hybrid stochastic systems. First, the concepts of synchronous and asynchronous switching parameters to the system states are proposed for a generalization of the asynchronous control. As preliminaries, a hybrid nonlinear differential inequality is established for coping with the synchronous models, and the [Formula: see text]-continuity of the system parameters driven by Markov chains is established for coping with the asynchronous models by the attribute of Markov chains for less conservativeness. Second, stability criteria with moment exponential estimates are established for two kinds of system models under the nonlinear growth condition. Third, the stabilization problem is illustrated based on the stability criteria and Riccati like matrix equations. A corollary is given to improve some stability theorems obtained in the related literature. New initial condition is formally proposed and explained for the nonlinear stochastic systems. Finally, a numerical example with simulation is proposed to illustrate the method, verify the conclusions of this article, and show the superiority of this work.

Adaptive Neural Event-Triggered Control of Networked Markov Jump Systems Under Hybrid Cyberattacks.

This article is concerned with the neural network (NN)-based event-triggered control problem for discrete-time networked Markov jump systems with hybrid cyberattacks and unmeasured states. The event-triggered mechanism (ETM) is used to reduce the communication load, and a Luenberger observer is introduced to estimate the unmeasured states. Two kinds of cyberattacks, denial-of-service (DoS) attacks and deception attacks, are investigated due to the vulnerability of cyberlayer. For the sake of mitigating the impact of these two types of cyberattacks on system performance, the ETM under DoS jamming attacks is discussed first, and a new estimation of such mechanism is given. Then, the NN technique is applied to approximate the injected false information. Some sufficient conditions are derived to guarantee the boundedness of the closed-loop system, and the observer and controller gains are presented by solving a set of matrix inequalities. The effectiveness of the presented control method is demonstrated by a numerical example.

Event-Triggered and Self-Triggered L∞ Control for Markov Jump Stochastic Nonlinear Systems Under DoS Attacks.

This article investigates event-triggered and self-triggered L∞ control problems for the Markov jump stochastic nonlinear systems subject to denial-of-service (DoS) attacks. When attacks prevent system devices from obtaining valid information over networks, a new switched model with unstable subsystems is constructed to characterize the effect of DoS attacks. On the basis of the switched model, a multiple Lyapunov function method is utilized and a set of sufficient conditions incorporating the event-triggering scheme (ETS) and restriction of DoS attacks are provided to preserve L∞ performance. In particular, considering that ETS based on mathematical expectation is difficult to be implemented on a practical platform, a self-triggering scheme (STS) without mathematical expectation is presented. Meanwhile, to avoid the Zeno behavior resulted from general exogenous disturbance, a positive lower bound is fixed in STS in advance. In addition, the exponent parameters are designed in STS to reduce triggering frequency. Based on the STS, the mean-square asymptotical stability and almost sure exponential stability are both discussed when the system is in the absence of exogenous disturbance. Finally, two examples are given to substantiate the effectiveness of the proposed method.

H∞ Control for Stochastic Singular Systems With Time-Varying Delays via Sampled-Data Controller.

In this article, H∞ control for stochastic singular time-varying delay systems under arbitrarily variable samplings is addressed via designing a sampled-data controller. The first and foremost, a novel time-dependent discontinuous Lyapunov-Krasovskii (L-K) functional is built, which takes good advantage of the factual sampling pattern's available properties. Then, based on the refined input delay method by utilizing the constructed time-dependent L-K functional, the free-weighting matrix method, and the auxiliary vector function approach are adopted to develop conditions ensuring the stochastic admissibility for the studied stochastic singular systems with time-varying delays. On the basis of the derived conditions, the sampled-data H∞ control issue is tackled, and an unambiguous expression for the sampled-data controller design method is obtained. Finally, simulation examples manifest that our proposed results are correct and effective.

Adaptive Neural State Estimation of Markov Jump Systems Under Scheduling Protocols and Probabilistic Deception Attacks.

The neural-network (NN)-based state estimation issue of Markov jump systems (MJSs) subject to communication protocols and deception attacks is addressed in this article. For relieving communication burden and preventing possible data collisions, two types of scheduling protocols, namely: 1) the Round-Robin (RR) protocol and 2) weighted try-once-discard (WTOD) protocol, are applied, respectively, to coordinate the transmission sequence. In addition, considering that the communication channel may suffer from mode-dependent probabilistic deception attacks, a hidden Markov-like model is proposed to characterize the relationship between the malicious signal and system mode. Then, a novel adaptive neural state estimator is presented to reconstruct the system states. By taking the influence of deception attacks into performance analysis, sufficient conditions under two different scheduling protocols are derived, respectively, so as to ensure the ultimately boundedness of the estimate error. In the end, simulation results testify the correctness of the adaptive neural estimator design method proposed in this article.

Design, Analysis, and Application of a Discrete Error Redefinition Neural Network for Time-Varying Quadratic Programming.

Time-varying quadratic programming (TV-QP) is widely used in artificial intelligence, robotics, and many other fields. To solve this important problem, a novel discrete error redefinition neural network (D-ERNN) is proposed. By redefining the error monitoring function and discretization, the proposed neural network is superior to some traditional neural networks in terms of convergence speed, robustness, and overshoot. Compared with the continuous ERNN, the proposed discrete neural network is more suitable for computer implementation. Unlike continuous neural networks, this article also analyzes and proves how to select the parameters and step size of the proposed neural networks to ensure the reliability of the network. Moreover, how to achieve the discretization of the ERNN is presented and discussed. The convergence of the proposed neural network without disturbance is proven, and bounded time-varying disturbances can be resisted in theory. Furthermore, the comparison results with other related neural networks show that the proposed D-ERNN has a faster convergence speed, better antidisturbance ability, and lower overshoot.

Relative States-Based Consensus for Sampled-Data Second-Order Multiagent Systems With Time-Varying Topology and Delays.

In this article, the consensus problem of sampled-data second-order integrator multiagent systems with switching topology and time-varying delay is studied. And, a zero rendezvous speed is not required in the problem. Two new consensus protocols that employ no absolute states are proposed, depending on the presence of delay. Sufficient synchronization conditions are obtained for both protocols. It is shown that consensus can be reached, provided there is a sufficiently small gain and periodically joint connectivity in the sense of scrambling graph or spanning tree. Finally, both numerical and practical examples are supplied for illustrative purpose, and both show the effectiveness of the theoretical results.

Event-Triggered Resilient L∞ Control for Markov Jump Systems Subject to Denial-of-Service Jamming Attacks.

In this article, the event-triggered resilient L∞ control problem is concerned for the Markov jump systems in the presence of denial-of-service (DoS) jamming attacks. First, a fixed lower bound-based event-triggering scheme (ETS) is presented in order to avoid the Zeno problem caused by exogenous disturbance. Second, when DoS jamming attacks are involved, the transmitted data are blocked and the old control input is kept by using the zero-order holder (ZOH). On the basis of this process, the effect of DoS attacks on ETS is further discussed. Next, by utilizing the state-feedback controller and multiple Lyapunov functions method, some criteria incorporating the restriction of DoS jamming attacks are proposed to guarantee the L∞ control performance of the event-triggered Markov closed-loop jump system. In particular, the bounded transition rates rather than the exact ones are taken into account. That is appropriate for the practical environment in which transition rates of the Markov process are difficult to measure accurately. Correspondingly, some criteria are proposed to obtain state-feedback gains and event-triggering parameters simultaneously. Finally, we provide two examples to show the effectiveness of the proposed method.

Dynamic Consensus of Second-Order Networked Multiagent Systems With Switching Topology and Time-Varying Delays.

This article investigates the dynamic consensus problem for the discrete-time second-order integrator networked multiagent system with time-varying delay and switching topology, in which the speed of each agent is not required to be synchronized to zero value. Novel consensus protocols using only relative state information are proposed, and sufficient conditions for dynamic consensus are derived. The results show that consensus can be reached for both the case with delay and the case without delay, if the gain is sufficiently small and the union of interaction graphs is scrambling or contains a spanning tree frequently enough as the system evolves. Numerical examples demonstrate the effectiveness of the theoretical results.

Filtering for Discrete-Time Takagi-Sugeno Fuzzy Nonhomogeneous Markov Jump Systems With Quantization Effects.

This article deals with the problem of H∞ and l2-l∞ filtering for discrete-time Takagi-Sugeno fuzzy nonhomogeneous Markov jump systems with quantization effects, respectively. The time-varying transition probabilities are in a polytope set. To reduce conservativeness, a mode-dependent logarithmic quantizer is considered in this article. Based on the fuzzy-rule-dependent Lyapunov function, sufficient conditions are given such that the filtering error system is stochastically stable and has a prescribed H∞ or l2-l∞ performance index, respectively. Finally, a practical example is provided to illustrate the effectiveness of the proposed fuzzy filter design methods.

Cluster consensus of nonlinear multi-agent systems with Markovian switching topologies and communication noises.

This paper focuses on the mean square cluster consensus of nonlinear multi-agent systems with Markovian switching topologies and communication noise via pinning control technique. Network topology can take weaker conditions in each cluster but an extra balanced condition is also needed. A time-varying control gain will be introduced to eliminate the effect of stochastic noise. For the case of fixed topology, if the induced digraph of each cluster has a directed spanning tree, the sufficient conditions for the mean square cluster consensus can be obtained. For the case of Markovian switching topologies, if the induced digraph of union of the Laplacian matrix of each mode has a directed spanning tree, the mean square cluster consensus conclusion can be derived. Particularly, if the elements of transition probability of Markov chain are partly unknown, we can also obtain the same conclusion under the same conditions. Finally, two examples are given to illustrate our results.

Synchronization of Stochastic Complex Dynamical Networks Subject to Consecutive Packet Dropouts.

This paper studies the modeling and synchronization problems for stochastic complex dynamical networks subject to consecutive packet dropouts. Different from some existing research results, both probability characteristic and upper bound of consecutive packet dropouts are involved in the proposed approach of controller design. First, an error dynamical network with stochastic and bounded delay is established by step-delay method, where the randomness of the bounded delay can be verified later by the probability theory method. A new modeling method is introduced to reflect the probability characteristic of consecutive packet dropouts. Based on the proposed model, some sufficient conditions are proposed under which the error dynamical network is globally exponentially synchronized in the mean square sense. Subsequently, a probability-distribution-dependent controller design procedure is then proposed. Finally, two numerical examples with simulations are provided to validate the analytical results and demonstrate the less conservatism of the proposed model method.

Necessary and Sufficient Conditions for Consensus of Continuous-Time Multiagent Systems With Markovian Switching Topologies and Communication Noises.

This paper investigates the mean square consensus problem for continuous-time multiagent systems with randomly switching topologies and noises. The switching is governed by a time-homogeneous Markov process, and each topology corresponds to a state of the process. Meanwhile, the communication noises are also considered for practical applications. We introduce a time-varying gain which can reduce the effect of communication noises. It is shown that the effect of Markovian switching topologies mainly depends on the union of topologies associated with the positive recurrent states of the Markov process. Then, necessary and sufficient conditions can be obtained under a control protocol with time-varying gain. Moreover, we extend our result to the cases where the topological structure is semi-Markovian switching and the elements of transition rate matrix are partly unknown. Finally, we give an example to illustrate the validity of our results.

Mean square consensus of leader-following multi-agent systems with measurement noises and time delays.

This paper investigates the mean square consensus problem of dynamical networks of leader-following multi-agent systems with measurement noises and time-varying delays. We consider that the fixed undirected communication topologies are connected. A neighbor-based tracking algorithm together with distributed estimators are presented. Using tools of algebraic graph theory and the Gronwall-Bellman-Halanay type inequality, we establish sufficient conditions to reach consensus in mean square sense via the proposed consensus protocols. Finally, a numerical simulation is provided to demonstrate the effectiveness of the obtained theoretical result.