H∞ synchronization of chaotic neural networks with time-varying delays

In this paper,we investigate the problem of H∞ synchronization for chaotic neural networks with time-varying delays.A new model of the networks with disturbances in both master and slave systems is presented.By constructing a suitable Lyapunov–Krasovskii functional and using a reciprocally convex approach,a novel H∞ synchronization criterion for the networks concerned is established in terms of linear matrix inequalities(LMIs)which can be easily solved by various effective optimization algorithms.Two numerical examples are given to illustrate the effectiveness of the proposed method.     

H_∞ synchronization of the coronary artery system with input time-varying delay

This paper investigates the H_∞ synchronization of the coronary artery system with input delay and disturbance.We focus on reducing the conservatism of existing synchronization strategies.Base on the triple integral forms of the Lyapunov–Krasovskii functional(LKF),we utilize single and double integral forms of Wirtinger-based inequality to guarantee that the synchronization feedback controller has good performance against time-varying delay and external disturbance.The effectiveness of our strategy can be exhibited by simulations under the different time-varying delays and different disturbances.     

Exponential synchronization of chaotic Lur’e systems with time-varying delay via sampled-data control

In this paper, we study the exponential synchronization of chaotic Lur＇e systems with time-varying delays via sampled-data control by using sector nonlinearties. In order to make full use of information about sampling intervals and interval time-varying delays, new Lyapunov-Krasovskii functionals with triple integral terms are introduced. Based on the convex combination technique, two kinds of synchronization criteria are derived in terms of linear matrix inequal- ities, which can be efficiently solved via standard numerical software. Finally, three numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed results.     

Robust H_∞ observer-based control for synchronization of a class of complex dynamical networks

This paper is concerned with the robust H∞ synchronization problem for a class of complex dynamical networks by applying the observer-based control. The proposed feedback control scheme is developed to ensure the asymptotic stability of the augmented system, to reconstruct the non-measurable state variables of each node and to improve the H∞ performance related to the synchronization error and observation error despite the external disturbance. Based on the Lyapunov stability theory, a synchronization criterion is obtained under which the controlled network can be robustly stabilized onto a desired state with a guaranteed H∞ performance. The controller and the observer gains can be given by the feasible solutions of a set of linear matrix inequalities (LMIs). The effectiveness of the proposed control scheme is demonstrated by a numerical example through simulation.     

Does synchronization of networks of chaotic maps lead to control?

We consider networks of chaotic maps with different network topologies. In each case, they are coupled in such a way as to generate synchronized chaotic solutions. By using the methods of control of chaos we are controlling a single map into a predetermined trajectory. We analyze the reaction of the network to such a control. Specifically we show that a line of one-dimensional logistic maps that are unidirectionally coupled can be controlled from the first oscillator whereas a ring of diffusively coupled maps cannot be controlled for more than 5 maps. We show that rings with more elements can be controlled if every third map is controlled. The dependence of unidirectionally coupled maps on noise is studied. The noise level leads to a finite synchronization lengths for which maps can be controlled by a single location. A two-dimensional lattice is also studied.     

Distributed H_∞ control of multi-agent systems with directed networks

This paper studies the distributed H∞control problem of identical linear time invariant multi-agent systems subject to external disturbances. A directed graph containing a spanning tree is used to model the communication topology. Based on the relative states of the neighbor agents and a subset of absolute states of the agents, distributed static H∞controllers are proposed. The concept of an H∞performance region is extended to the directed graph situation. Then the results are used to solve the leader–follower H∞consensus problem. Sufficient conditions are proposed based on bounded real lemma and algebraic graph theory. The effectiveness of the theoretical results is illustrated via numerical simulations.     

The H_∞ synchronization of nonlinear Bloch systems via dynamic feedback control approach

We consider an H ∞ synchronization problem in nonlinear Bloch systems.Based on Lyapunov stability theory and linear matrix inequality formulation,a dynamic feedback controller is designed to guarantee asymptotic stability of the master-slave synchronization.Moreover,this controller reduces the effect of an external disturbance to the H ∞ norm constraint.A numerical example is given to validate the proposed synchronization scheme.     

Robust H_∞ control of uncertain systems with two additive time-varying delays

This paper is concerned with the problem of delay-dependent robust H∞control for a class of uncertain systems with two additive time-varying delays. A new suitable Lyapunov–Krasovskii functional(LKF) with triple integral terms is constructed and a tighter upper bound of the derivative of the LKF is derived. By applying a convex optimization technique, new delay-dependent robust H∞stability criteria are derived in terms of linear matrix inequalities(LMI). Based on the stability criteria, a state feedback controller is designed such that the closed-loop system is asymptotically stable.Finally, numerical examples are given to illustrate the effectiveness of the proposed method. Comparison results show that our results are less conservative than the existing methods.     

Robust H_∞ control of piecewise-linear chaotic systems with random data loss

<正>This paper studies the problem of robust H_∞control of piecewise-linear chaotic systems with random data loss. The communication links between the plant and the controller are assumed to be imperfect(that is,data loss occurs intermittently,which appears typically in a network environment).The data loss is modelled as a random process which obeys a Bernoulli distribution.In the face of random data loss,a piecewise controller is designed to robustly stabilize the networked system in the sense of mean square and also achieve a prescribed H_∞disturbance attenuation performance based on a piecewise-quadratic Lyapunov function.The required H_∞controllers can be designed by solving a set of linear matrix inequalities(LMIs).Chua's system is provided to illustrate the usefulness and applicability of the developed theoretical results.     

Robust H∞ observer-based of a class of complex control for synchronization dynamical networks

This paper is concerned with the robust Hoo synchronization problem for a class of complex dynamical networks by applying the observer-based control. The proposed feedback control scheme is developed to ensure the asymptotic stability of the augmented system, to reconstruct the non-measurable state variables of each node and to improve the H∞ performance related to the synchronization error and observation error despite the external disturbance. Based on the Lyapunov stability theory, a synchronization criterion is obtained under which the controlled network can be robustly stabilized onto a desired state with a guaranteed H∞ performance. The controller and the observer gains can be given by the feasible solutions of a set of linear matrix inequalities （LMIs）. The effectiveness of the proposed control scheme is demonstrated by a numerical example through simulation.     

Augmented Lyapunov approach to H_∞ state estimation of static neural networks with discrete and distributed time-varying delays

This paper deals with H∞state estimation problem of neural networks with discrete and distributed time-varying delays. A novel delay-dependent concept of H∞state estimation is proposed to estimate the H∞performance and global asymptotic stability of the concerned neural networks. By constructing the Lyapunov–Krasovskii functional and using the linear matrix inequality technique, sufficient conditions for delay-dependent H∞performances are obtained, which can be easily solved by some standard numerical algorithms. Finally, numerical examples are given to illustrate the usefulness and effectiveness of the proposed theoretical results.     

Robust H_∞ cluster synchronization analysis of Lurie dynamical networks

The cluster synchronization problem of complex dynamical networks with each node being a Lurie system with exter- nal disturbances and time-varying delay is investigated in this paper. Some criteria for cluster synchronization with desired H∞ performance are presented by using a local linear control scheme. Firstly, sufficient conditions are established to realize cluster synchronization of the Lurie dynamical networks without time delay. Then, the notion of the cluster synchronized region is introduced, and some conditions guaranteeing the cluster synchronized region and unbounded cluster synchro- nized region are derived. Furthermore, the cluster synchronization and cluster synchronized region in the Lurie dynamical networks with time-varying delay are considered. Numerical examples are finally provided to verify and illustrate the theoretical results.     

Complete synchronization of uncertain chaotic dynamical network via a simple adaptive control

In this paper, based on the invaxiance principle of differential equations, we propose a simple adaptive control method to synchronize the network with coupling of the general form. Comparing with other control approaches, this scheme only depends on each node＇s state output. So we need not to know the concrete network structure and the solutions of the isolate nodes of the network in advance. In order to demonstrate the effectiveness of the method, a special example is provided and numerical simulations are performed. The numerical results show that our control scheme is very effective and robust against the weak noise.     

Adaptive synchronization of a critical chaotic system

This paper further investigates the synchronization problem of a new chaotic system with known or unknown system parameters. Based on the Lyapunov stability theory, a novel adaptive control law is derived for the synchronization of a new chaotic system with known or unknown system parameters. Theoretical analysis and numerical simulations show the effectiveness and feasibility of the proposed schemes.     

Robust adaptive synchronization of chaotic neural networks by slide technique

In this paper, we focus on the robust adaptive synchronization between two coupled chaotic neural networks with all the parameters unknown and time-varying delay. In order to increase the robustness of the two coupled neural networks, the key idea is that a sliding-mode-type controller is employed. Moreover, without the estimate values of the network unknown parameters taken as an updating object, a new updating object is introduced in the constructing of controller. Using the proposed controller, without any requirements for the boundedness, monotonicity and differentiability of activation functions, and symmetry of connections, the two coupled chaotic neural networks can achieve global robust synchronization no matter what their initial states are. Finally, the numerical simulation validates the effectiveness and feasibility of the proposed technique.     

Impulsive control for synchronization of nonlinear Rossler chaotic systems

This paper reports that an impulsive control theory for synchronization of nonlinear R?ssler chaotic systems is developed. A new framework for impulsive synchronization between such chaotic systems is presented, which makes the synchronization error system a linear impulsive control system. Therefore, it is easy to derive the impulsive synchronization law. The proposed impulsive control scheme is illustrated by nonlinear R?ssler chaotic systems and the simulation results demonstrate the effectiveness of the method.     

Improved delay-dependent robust H_∞ control of an uncertain stochastic system with interval time-varying and distributed delays

In this paper, the robust H∞control problem for a class of stochastic systems with interval time-varying and distributed delays is discussed. The system under study involves parameter uncertainty, stochastic disturbance, interval time-varying,and distributed delay. The aim is to design a delay-dependent robust H∞control which ensures the robust asymptotic stability of the given system and to express it in the form of linear matrix inequalities（LMIs）. Numerical examples are given to demonstrate the effectiveness of the proposed method. The results are also compared with the existing results to show its conservativeness.     

Finite-time Mittag—Leffler synchronization of fractional-order complex-valued memristive neural networks with time delay

Without dividing the complex-valued systems into two real-valued ones, a class of fractional-order complex-valued memristive neural networks (FCVMNNs) with time delay is investigated. Firstly, based on the complex-valued sign function, a novel complex-valued feedback controller is devised to research such systems. Under the framework of Filippov solution, differential inclusion theory and Lyapunov stability theorem, the finite-time Mittag—Leffler synchronization (FTMLS) of FCVMNNs with time delay can be realized. Meanwhile, the upper bound of the synchronization settling time (SST) is less conservative than previous results. In addition, by adjusting controller parameters, the global asymptotic synchronization of FCVMNNs with time delay can also be realized, which improves and enrich some existing results. Lastly, some simulation examples are designed to verify the validity of conclusions.     

Robust H_∞ control for uncertain systems with heterogeneous time-varying delays via static output feedback

This paper is concerned with the problem of robust H∞ control for a novel class of uncertain linear continuous-time systems with heterogeneous time-varying state/input delays and norm-bounded parameter uncertainties.The objective is to design a static output feedback controller such that the closed-loop system is asymptotically stable while satisfying a prescribed H∞ performance level for all admissible uncertainties.By constructing an appropriate Lyapunov-Krasvskii functional,a delay-dependent stability criterion of the closed-loop system is presented with the help of the Jensen integral inequality.From the derived criterion,the solutions to the problem are formulated in terms of linear matrix inequalities and hence are tractable numerically.A simulation example is given to illustrate the effectiveness of the proposed design method.