Exponential stability via aperiodically intermittent control of complex-variable time delayed chaotic systems

summary:This paper focuses on the problem of exponential stability analysis of uncertain complex-variable time delayed chaotic systems, where the parameters perturbation are bounded assumed. The aperiodically intermittent control strategy is proposed to stabilize the complex-variable delayed systems. By taking the advantage of Lyapunov method in complex field and utilizing inequality technology, some sufficient conditions are derived to ensure the stability of uncertain complex-variable delayed systems, where the constrained time delay are considered in the conditions obtained. To protrude the availability of the devised stability scheme, simulation examples are ultimately demonstrated

Synchronization of chaotic delayed systems via intermittent control and its adaptive strategy

In this paper the problem of synchronization for delayed chaotic systems is considered based on aperiodic intermittent control. First, delayed chaotic systems are proposed via aperiodic adaptive intermittent control. Next, to cut down the control gain, a new generalized intermittent control and its adaptive strategy is introduced. Then, by constructing a piecewise Lyapunov auxiliary function and making use of piecewise analysis technique, some effective and novel criteria are obtained to ensure the global synchronization of delayed chaotic systems by means of the designed control protocols. At the end, two examples with numerical simulations are provided to verify the effectiveness of the theoretical results proposed scheme

Weighted Sum Synchronization of Memristive Coupled Neural Networks

Funding Information: This work is supported by the National Natural Science Foundation of China (No. 61971185) and the Open Fund Project of Key Laboratory in Hunan Universities (No. 18K010). Publisher Copyright: © 2020 Elsevier B.V.It is well known that weighted sum of node states plays an essential role in function implementation of neural networks. Therefore, this paper proposes a new weighted sum synchronization model for memristive neural networks. Unlike the existing synchronization models of memristive neural networks which control each network node to reach synchronization, the proposed model treats the networks as dynamic entireties by weighted sum of node states and makes the entireties instead of each node reach expected synchronization. In this paper, weighted sum complete synchronization and quasi-synchronization are both investigated by designing feedback controller and aperiodically intermittent controller, respectively. Meanwhile, a flexible control scheme is designed for the proposed model by utilizing some switching parameters and can improve anti-interference ability of control system. By applying Lyapunov method and some differential inequalities, some effective criteria are derived to ensure the synchronizations of memristive neural networks. Moreover, the error level of the quasi-synchronization is given. Finally, numerical simulation examples are used to certify the effectiveness of the derived results.Peer reviewe

Impulsive mean square exponential synchronization of stochastic dynamical networks with hybrid time-varying delays

This paper investigates the mean square exponential synchronization problem for complex dynamical networks with stochastic disturbances and hybrid time-varying delays, both internal delay and coupling delay are considered in the model. At the same time, the coupled time-delay is also probabilistic in two time interval. Impulsive control method is applied to force all nodes synchronize to a chaotic orbit, and impulsive input delay is also taken into account. Based on the theory of stochastic differential equation, an impulsive differential inequality and some analysis techniques, several simple and useful criteria are derived to ensure mean square exponential synchronization of the stochastic dynamical networks. Furthermore, pinning impulsive strategy is studied. An effective method is introduced to select the controlled nodes at each impulsive constants. Numerical simulations are exploited to demonstrate the effectiveness of the theory results in this paper

Synchronization Control for Discrete-Time-Delayed Dynamical Networks with Switching Topology under Actuator Saturations

10.13039/501100001809-National Natural Science Foundation of China (Grant Number: 61773156, 61873148, 61673141 and 61933007); 10.13039/501100018551-Program for Science and Technology Innovation Talents in the Universities of Henan Province of China (Grant Number: 19HASTIT028); 10.13039/501100010029-Research Fund for the Taishan Scholar Project of Shandong Province of China; 10.13039/501100000288-Royal Society of the U.K.; 10.13039/100005156-Alexander von Humboldt Foundation of Germany

Engineering Emergence: A Survey on Control in the World of Complex Networks

Complex networks make an enticing research topic that has been increasingly attracting researchers from control systems and various other domains over the last two decades. The aim of this paper was to survey the interest in control related to complex networks research over time since 2000 and to identify recent trends that may generate new research directions. The survey was performed for Web of Science, Scopus, and IEEEXplore publications related to complex networks. Based on our findings, we raised several questions and highlighted ongoing interests in the control of complex networks.publishedVersio

Impulsive Control of Dynamical Networks

Dynamical networks (DNs) consist of a large set of interconnected nodes with each node being a fundamental unit with detailed contents. A great number of natural and man-made networks such as social networks, food networks, neural networks, WorldWideWeb, electrical power grid, etc., can be effectively modeled by DNs. The main focus of the present thesis is on delay-dependent impulsive control of DNs. To study the impulsive control problem of DNs, we firstly construct stability results for general nonlinear time-delay systems with delayed impulses by using the method of Lyapunov functionals and Razumikhin technique. Secondly, we study the consensus problem of multi-agent systems with both fixed and switching topologies. A hybrid consensus protocol is proposed to take into consideration of continuous-time communications among agents and delayed instant information exchanges on a sequence of discrete times. Then, a novel hybrid consensus protocol with dynamically changing interaction topologies is designed to take the time-delay into account in both the continuous-time communication among agents and the instant information exchange at discrete moments. We also study the consensus problem of networked multi-agent systems. Distributed delays are considered in both the agent dynamics and the proposed impulsive consensus protocols. Lastly, stabilization and synchronization problems of DNs under pinning impulsive control are studied. A pinning algorithm is incorporated with the impulsive control method. We propose a delay-dependent pinning impulsive controller to investigate the synchronization of linear delay-free DNs on time scales. Then, we apply the pinning impulsive controller proposed for the delay-free networks to stabilize time-delay DNs. Results show that the delay-dependent pinning impulsive controller can successfully stabilize and synchronize DNs with/without time-delay. Moreover, we design a type of pinning impulsive controllers that relies only on the network states at history moments (not on the states at each impulsive instant). Sufficient conditions on stabilization of time-delay networks are obtained, and results show that the proposed pinning impulsive controller can effectively stabilize the network even though only time-delay states are available to the pinning controller at each impulsive instant. We further consider the pinning impulsive controllers with both discrete and distributed time-delay effects to synchronize the drive and response systems modeled by globally Lipschitz time-delay systems. As an extension study of pinning impulsive control approach, we investigate the synchronization problem of systems and networks governed by PDEs

Robust Control

The need to be tolerant to changes in the control systems or in the operational environment of systems subject to unknown disturbances has generated new control methods that are able to deal with the non-parametrized disturbances of systems, without adapting itself to the system uncertainty but rather providing stability in the presence of errors bound in a model. With this approach in mind and with the intention to exemplify robust control applications, this book includes selected chapters that describe models of H-infinity loop, robust stability and uncertainty, among others. Each robust control method and model discussed in this book is illustrated by a relevant example that serves as an overview of the theoretical and practical method in robust control