D. H. Ji

Adaptive lag synchronization for uncertain complex dynamical network with delayed coupling

Abstract This paper proposes an adaptive control method to achieve the lag synchronization between uncertain complex dynamical network having delayed coupling and a non-identical reference node. Unknown parameters of both the network and reference node are estimated by adaptive laws obtained by Lyapunov stability theory. With the estimated parameters, the proposed method guarantees the globally asymptotical synchronization of the network in spite of unknown bounded disturbances. The effectiveness of our work is verified through a numerical example and simulation.

Passivity-based control for Hopfield neural networks using convex representation

This paper considers the problem of passivity-based controller design for Hopfield neural networks. By making use of a convex representation of nonlinearities, a feedback control scheme based on passivity and Lyapunov theory is presented. A criterion for existence of the controller is given in terms of linear matrix inequality (LMI), which can be easily solved by a convex optimization problem. An example and its numerical simulation are given to show the effectiveness of the proposed method.

Guaranteed cost synchronization of a complex dynamical network via dynamic feedback control

Abstract In this paper, the problem of guaranteed cost synchronization for a complex network is investigated. In order to achieve the synchronization, two types of guaranteed cost dynamic feedback controller are designed. Based on Lyapunov stability theory, a linear matrix inequality (LMI) convex optimization problem is formulated to find the controller which guarantees the asymptotic stability and minimizes the upper bound of a given quadratic cost function. Finally, a numerical example is given to illustrate the proposed method.

Synchronization of singular complex dynamical networks with time-varying delays

Abstract This paper considers delay dependent synchronizations of singular complex dynamical networks with time-varying delays. A modified Lyapunov–Krasovskii functional is used to derive a sufficient condition for synchronization in terms of LMIs (linear matrix inequalities) which can be easily solved by various convex optimization algorithms. Numerical examples show the effectiveness of the proposed method.

Decentralized guaranteed cost dynamic control for synchronization of a complex dynamical network with randomly switching topology

This paper considers synchronization problem of a complex dynamical network. For this problem, a decentralized guaranteed cost dynamic feedback controller is designed to achieve the synchronization of the network. Based on Lyapunov stability theory and linear matrix inequality framework, the existence condition for feasible controllers is derived in terms of linear matrix inequalities. Finally, the proposed method is applied to two numerical examples in order to show the effectiveness of our result.

Adaptive synchronization for uncertain chaotic neural networks with mixed time delays using fuzzy disturbance observer

This paper proposes a robust adaptive control method for synchronization of uncertain chaotic neural networks with mixed delays. Uncertainty and disturbance in the networks are estimated by fuzzy disturbance observer without any prior information about them. The proposed control scheme with adaptive laws is derived based on Lyapunov-Krasovskii stability theory to guarantee the globally asymptotical synchronization between the networks. An example is illustrated to show the effectiveness of the proposed method.

Leader-following consensus problem of heterogeneous multi-agent systems with nonlinear dynamics using fuzzy disturbance observer

This article considers the leader-following consensus problem of heterogeneous multi-agent systems. The proposed multi-agent system is consisted of heterogeneous agents where each agents have their own nonlinear dynamic behavior. To overcome difficulty from heterogeneous nonlinear intrinsic dynamics of agents, a fuzzy disturbance observer is adopted. In addition, based on the Lyapunov stability theory, an adaptive control method is used to compensate the observation error caused by the difference between the unknown factor and estimated values. Two numerical examples are given to illustrate the effectiveness of the proposed method.

Synchronization Criterion for Lur’e Systems via Delayed PD Controller

In this paper, the effects of a time varying delay on a chaotic drive-response synchronization are considered. Using a delayed feedback proportional-derivative (PD) controller scheme, a delay-dependent synchronization criterion is derived for chaotic systems represented by the Lur’e system with sector and slope restricted nonlinearities. The derived criterion is a sufficient condition for the absolute stability of the error dynamics between the drive and the response systems. By the use of a convex representation of the nonlinearity and the discretized Lyapunov-Krasovskii functional, stability condition is obtained via the LMI formulation. The condition represented in the terms of linear matrix inequalities (LMIs) can be solved by the application of convex optimization algorithms. The effectiveness of the work is verified through numerical examples.

Integral control for synchronization of complex dynamical networks with unknown non-identical nodes

This paper proposes a high gain integral controller for synchronization of complex dynamical networks with unknown non-identical nodes. The integral controller converts the complex dynamical system into a singular perturbation form. Then, a sufficient condition for global synchronization is derived. Finally, the numerical simulation is presented to illustrate the effectiveness of the proposed method.

Robust H∞ filtering for a class of discrete-time nonlinear systems

Abstract In this paper, a robust H ∞ filtering problem is considered for a class of discrete-time nonlinear systems. Based on the Lyapunov method, a design criterion of the robust H ∞ filter guarantee not only the stability but also the prespecified upper bound of H ∞ norm from the disturbance inputs to error state outputs. The design condition can be solved easily by efficient convex optimization algorithms. Numerical examples show the effectiveness of the proposed method.