Fixed-Time Stochastic Synchronization of Complex Networks via Continuous Control

Novel adaptive synchronization in finite-time and fixed-time for impulsive complex networks with semi-Markovian switching

This paper intensively studied the finite-time (FNT) and fixed-time (FXT) synchronization issues for complex networks (CNs) with semi-Markovian switching and impulsive effect. The impulses are assumed to be independent of the semi-Markovian switching. Firstly, a unified FNT and FXT stability criterion of impulsive dynamical system with time-varying delays is extended by comparison principle. Secondly, two novel hybrid control schemes, which are composed of adaptive gain and switching state-feedback are proposed. Thirdly, by employing Kronecker product, Lyapunov-Krasovskii functional and inequality technique, FNT and FXT synchronization criteria for impulsive CNs with semi-Markovian switching are presented in a set of low-dimensional linear matrix inequalities, and the settling times are computed respectively. Finally, simulations are given to verify the proposed adaptive FNT and FXT synchronization criteria.

New results on adaptive fixed-time control for convex-delayed neural networks

This paper studies the adaptive fixed-time synchronization issue for convex-delayed neural networks. First, the convex delay is introduced to address the state delay of neural networks in order to reflect the impacts of multiple delay components such as input transition time and switching communication. Then, a new fixed-time control method is presented to adaptively determine multi-control gains with a unified update law. Afterward, some sufficient criteria are figured out by using Lyapunov stability theorem to ensure that the delayed neural networks are fixed-timely stable. Finally, simulated examples are adopted to validate our theoretical results.

Strictly intermittent quantized control for fixed/predefined-time cluster lag synchronization of stochastic multi-weighted complex networks

This article addresses the fixed-time (F-T) and predefined-time (P-T) cluster lag synchronization of stochastic multi-weighted complex networks (SMWCNs) via strictly intermittent quantized control (SIQC). Firstly, by exploiting mathematical induction and reduction to absurdity, a novel F-T stability lemma is proved and an accurate estimation of settling time (ST) is obtained. Subsequently, by virtue of the proposed F-T stability, some simple conditions that ensure the F-T cluster lag synchronization of SMWCNs are derived by developing a SIQC strategy. Furthermore, the P-T cluster lag synchronization is also explored based on a SIQC design, where the ST can be predefined by an adjustable constant of the controller. Note that the designed controllers here are simpler and more economical than the traditional design whose the linear part is still activated during the rest interval. Finally, two numerical examples are provided to verify the effectiveness of the theoretical results.

A Dynamic Event-Triggered Approach to Recursive Nonfragile Filtering for Complex Networks With Sensor Saturations and Switching Topologies

In this article, the nonfragile filtering issue is addressed for complex networks (CNs) with switching topologies, sensor saturations, and dynamic event-triggered communication protocol (DECP). Random variables obeying the Bernoulli distribution are utilized in characterizing the phenomena of switching topologies and stochastic gain variations. By introducing an auxiliary offset variable in the event-triggered condition, the DECP is adopted to reduce transmission frequency. The goal of this article is to develop a nonfragile filter framework for the considered CNs such that the upper bounds on the filtering error covariances are ensured. By the virtue of mathematical induction, gain parameters are explicitly derived via minimizing such upper bounds. Moreover, a new method of analyzing the boundedness of a given positive-definite matrix is presented to overcome the challenges resulting from the coupled interconnected nodes, and sufficient conditions are established to guarantee the mean-square boundedness of filtering errors. Finally, simulations are given to prove the usefulness of our developed filtering algorithm.

Analysis of random synchronization under bilayer derivative and nonlinear delay networks of neuron nodes via fixed time policies

In order to solve a challenging problem, i.e., fixed time synchronization of bilayer networks with derivative coupling and nonlinear delay coupling, fixed time polices are brought to achieve random synchronization for bilayer multiple weight hybrid coupled networks of neuron nodes. Being different from the synthesis method, which is often used to get theoretical conclusions from known conditions for synchronization of networks in general articles, analysis method is applied to seek parameters in fixed time controllers and sufficient conditions for synchronization from conclusions. After analysis, we obtain a relationship between coefficients of controllers and coefficients of a formula which is related to Lyapunov function. Moreover, we find that fixed settling time for synchronization is affected by the maximum eigenvalue of a matrix associated with network topology, parameters in the designed controllers and the size of networks. Finally, synchronous tests of bilayer networks of Hindmarsh-Rose (HR) neuron nodes are carried out to show the effectiveness of theoretical results.

Prefixed-Time Local Intermittent Sampling Synchronization of Stochastic Multicoupling Delay Reaction-Diffusion Dynamic Networks

This article focuses on the problem of prefixed-time synchronization for stochastic multicoupled delay dynamic networks with reaction-diffusion terms and discontinuous activation by means of local intermittent sampling control. Notably, unlike the existing common fixed-time synchronization, this article puts forward a new synchronization concept, prefixed-time synchronization, based on the fact that stochastic noise and discontinuous activation can be seen everywhere in practical engineering, which can effectively perfect and improve the existing works. Specifically, a local intermittent in the time domain and point sampling control strategy in the spatial domain is proposed instead of a simple single intermittent control approach, which greatly reduces the control cost. In addition, by some effective means, including the famous Young's inequality, Jensen's inequality, and Hölder's inequality, we obtain two different synchronization criteria of the networks without delay and with multicoupling delays and deeply reveal the quantitative relationship among control period, point sampling length, and network scale. Finally, a numerical example is given to verify the effectiveness of the developed method and the practicability by Chua's circuit model.

Intralayer Synchronization of Multiplex Dynamical Networks via Pinning Impulsive Control

These days, the synchronization of multiplex networks is an emerging and important research topic. Grounded framework and theory about synchronization and control on multiplex networks are yet to come. This article studies the intralayer synchronization on a multiplex network (i.e., a set of networks connected through interlayer edges), via the pinning impulsive control method. The topologies of different layers are independent of each other, and the individual dynamics of nodes in different layers are different as well. Supra-Laplacian matrices are adopted to represent the topological structures of multiplex networks. Two cases are considered according to impulsive sequences of multiplex networks: 1) pinning controllers are applied to all the layers simultaneously at the instants of a common impulse sequence and 2) pinning controllers are applied to each layer at the instants of distinct impulse sequences. Using the Lyapunov stability theory and the impulsive control theory, several intralayer synchronization criteria for multiplex networks are obtained, in terms of the supra-Laplacian matrix of network topology, self-dynamics of nodes, impulsive intervals, and the pinning control effect. Furthermore, the algorithms for implementing pinning schemes at every impulsive instant are proposed to support the obtained criteria. Finally, numerical examples are presented to demonstrate the effectiveness and correctness of the proposed schemes.

Distributed Event-Triggered Consensus of General Linear Multiagent Systems Under Directed Graphs

This article investigates the consensus problem of general linear multiagent systems under directed communication graphs with event-triggered mechanisms. First, a novel distributed static event-triggered mechanism with a state-dependent threshold is proposed to solve the consensus problem, both with a positive lower bound on the average time interval of the communication among agents and updates of controllers. Thus, the Zeno behavior is excluded for communication among agents and controller updates. Next, to further reduce the frequencies of communication among agents and updates of controllers, a distributed dynamic event-triggered mechanism is introduced. By applying the static and dynamic mechanisms, the problem can be addressed with the reduced use of system resources compared with that in most existing control algorithms. Finally, numerical simulations are presented to verify the effectiveness of the results.

Fixed/Preassigned-Time Synchronization of Complex Networks via Improving Fixed-Time Stability

This article is concerned with the problem of fixed-time (FXT) and preassigned-time (PAT) synchronization for discontinuous dynamic networks by improving FXT stability and developing simple control schemes. First, some more relaxed conditions for FXT stability are established and several more accurate estimates for the settling time (ST) are obtained by means of some special functions. Based on the improved FXT stability, FXT synchronization for discontinuous networks is discussed by designing a simple controller without a linear feedback term. Besides, the PAT synchronization is also explored by developing several nontrivial control protocols with finite control gains, where the synchronized time can be prespecified according to actual needs and is irrelevant with any initial value and any parameter. Finally, the improved FXT stability and the synchronization for complex networks are confirmed by two numerical examples.

Cluster synchronization of delayed coupled neural networks: Delay-dependent distributed impulsive control

This paper investigates the issue of cluster synchronization (CS) for the coupled neural networks (CNNs) with time-varying delays via the delay-dependent distributed impulsive control. A new Halanay-like inequality, where delayed impulses are taken into consideration, is proposed. Based on the Lyapunov theory and the new differential inequality, sufficient conditions of CS for delayed CNNs with fixed and switching coupling topology are obtained, respectively. Moreover, delay-dependent distributed impulsive controllers with fixed or switching topology are designed thereby. Finally, we present a numerical example of CNNs with fixed or switching coupling to verify the effectiveness of our results, respectively.

Finite-Horizon H∞ State Estimation for Stochastic Coupled Networks With Random Inner Couplings Using Round-Robin Protocol

This article is concerned with the problem of finite-horizon H_∞ state estimation for time-varying coupled stochastic networks through the round-robin scheduling protocol. The inner coupling strengths of the considered coupled networks are governed by a random sequence with known expectations and variances. For the sake of mitigating the occurrence probability of the network-induced phenomena, the communication network is equipped with the round-robin protocol that schedules the signal transmissions of the sensors' measurement outputs. By using some dedicated approximation techniques, an uncertain auxiliary system with stochastic parameters is established where the multiplicative noises enter the coefficient matrix of the augmented disturbances. With the established auxiliary system, the desired finite-horizon H_∞ state estimator is acquired by solving coupled backward Riccati equations, and the corresponding recursive estimator design algorithm is presented that is suitable for online application. The effectiveness of the proposed estimator design method is validated via a numerical example.

Anti-Synchronization in Fixed Time for Discontinuous Reaction-Diffusion Neural Networks With Time-Varying Coefficients and Time Delay

This paper studies the fixed-time anti-synchronization (FTAS) of discontinuous reaction-diffusion neural networks (DRDNNs) with both time-varying coefficients and time delay. First, differential inclusion theory is used to deal with the influence caused by discontinuous activations. In addition, a new fixed-time convergence theorem is used to handle the time-varying coefficients. Second, a novel state-feedback control algorithm and integral state-feedback control algorithm are proposed to realize FTAS of DRDNNs. During the generalized (adaptive) pinning control strategy, a guideline is proposed to select neurons to pin the designed controller. Furthermore, we present several criteria on FTAS by using the generalized Lyapunov function method. Different from the traditional Lyapunov function with negative definite derivative, the derivative of the Lyapunov function can be positive in this paper. Finally, we give two numerical simulations to substantiate the merits of the obtained results.

Finite-time and fixed-time anti-synchronization of Markovian neural networks with stochastic disturbances via switching control

This paper proposes a unified theoretical framework to study the problem of finite/fixed-time drive-response anti-synchronization for a class of Markovian stochastic neural networks. State feedback switching controllers without the sign function are designed to achieve the finite/fixed-time anti-synchronization of the addressed systems. Compared with the existing synchronization criteria, our results indicate that the controllers via the switching control without the sign function are given with less conservativeness, and the controllers without any sign function can deal with the chattering problem. By employing Lyapunov functional method and properties of the Weiner process, several finite/fixed-time synchronization criteria are presented and the corresponding settling times are calculated as well. Finally, three numerical examples are provided to illustrate the effectiveness of the theoretical results.