Chengdong Yang

Exponential synchronization for a class of complex spatio-temporal networks with space-varying coefficients

Abstract This paper addresses the problem of exponential synchronization for a class of complex spatio-temporal networks with space-varying coefficients, where the dynamics of nodes are described by coupled partial differential equations (PDEs). The goal of this research is to design distributed proportional-spatial derivative (P-sD) state feedback controllers to ensure exponential synchronization of the complex spatio-temporal network. Using Lyapunov׳s direct method, the problem of exponential synchronization of the complex spatio-temporal network is formulated as the feasibility problem of spatial differential linear matrix inequality (SDLMI) in space. The feasible solutions to this SDLMI in space can be approximately derived via the standard finite difference method and the linear matrix inequality (LMI) optimization technique. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed design method.

Existence and stability of periodic solution of high-order discrete-time Cohen–Grossberg neural networks with varying delays

Abstract This paper studies the existence and stability of periodic solution of the high-order discrete-time Cohen–Grossberg neural networks with varying delays. The properties of M-matrix and the contracting mapping principle are used to obtain a sufficient condition that guarantees the uniqueness and global exponential stability of the periodic solution. In addition, a numerical example is given that demonstrates the effectiveness of the proposed theoretical results.

Finite-time stability of genetic regulatory networks with impulsive effects

We study the finite-time stability of genetic regulatory networks with impulsive effects. Using the method of Lyapunov function, sufficient conditions of the finite-stability, in terms of linear matrix inequalities, are established. A numerical example is provided to further illustrate the significance of our results.

Robust Exponential Synchronization for a Class of Master-Slave Distributed Parameter Systems with Spatially Variable Coefficients and Nonlinear Perturbation

This paper addresses the exponential synchronization problem of a class of master-slave distributed parameter systems (DPSs) with spatially variable coefficients and spatiotemporally variable nonlinear perturbation, modeled by a couple of semilinear parabolic partial differential equations (PDEs). With a locally Lipschitz constraint, the perturbation is a continuous function of time, space, and system state. Firstly, a sufficient condition for the robust exponential synchronization of the unforced semilinear master-slave PDE systems is investigated for all admissible nonlinear perturbations. Secondly, a robust distributed proportional-spatial derivative (P-sD) state feedback controller is desired such that the closed-loop master-slave PDE systems achieve exponential synchronization. Using Lyapunov’s direct method and the technique of integration by parts, the main results of this paper are presented in terms of spatial differential linear matrix inequalities (SDLMIs). Finally, two numerical examples are provided to show the effectiveness of the proposed methods applied to the robust exponential synchronization problem of master-slave PDE systems with nonlinear perturbation.

Dynamic analysis of periodic solution for high-order discrete-time Cohen-Grossberg neural networks with time delays

In this paper, we analyze the dynamic behavior of periodic solution for the high-order discrete-time Cohen-Grossberg neural networks (CGNNs) with time delays. First, the existence is studied based on the continuation theorem of coincidence degree theory and Youngs inequality. And then, the criterion for the global exponential stability is given using Lyapunov method. Finally, simulation result shows the effectiveness of our proposed criterion.

Almost periodic dynamics of the delayed complex-valued recurrent neural networks with discontinuous activation functions

The target of this article is to study almost periodic dynamical behaviors for complex-valued recurrent neural networks with discontinuous activation functions and time-varying delays. We construct an equivalent discontinuous right-hand equation by decomposing real and imaginary parts of complex-valued neural networks. Based on differential inclusions theory, diagonal dominant principle and nonsmooth analysis theory of generalized Lyapunov function method, we achieve the existence, uniqueness and global stability of almost periodic solution for the equivalent delayed differential network. In particular, we derive a series of results on the equivalent neural networks with discontinuous activation functions, constant coefficients as well as periodic coefficients, respectively. Finally, we give a numerical example to demonstrate the effectiveness and feasibility of the derived theoretical results.

Synchronization for Nonlinear Complex Spatio-Temporal Networks with Multiple Time-Invariant Delays and Multiple Time-Varying Delays

This paper deals with the problem for synchronization of a nonlinear time delayed complex spatio-temporal network (CSN), modelled by semi-linear parabolic partial differential-difference equations. A boundary controller relying to distributed measurement is designed. Multiple time-invariant delays are firstly considered. By employing Lyapunov’s direct method and Wirtingers inequality, synchronization criteria of the CSN are presented in terms of LMIs. And then, multiple time-varying delays are respectively considered using the boundary controller and synchronization criteria are obtained. Finally, an example illustrates the effectiveness of the proposed method.

The Global Exponential Stability of the Delayed Complex-Valued Neural Networks with Almost Periodic Coefficients and Discontinuous Activations

In this paper, the almost periodic dynamical behaviors are considered for delayed complex-valued neural networks with discontinuous activation functions. We decomposed complex-valued to real and imaginary parts, and set an equivalent discontinuous right-hand equation. Depended on the differential inclusions theory, diagonal dominant principle, non-smooth analysis theory and generalized Lyapunov function, sufficient criteria are obtained for the existence uniqueness and global stability of almost periodic solution of the equivalent delayed differential system. Especially, we derive a series of results on the equivalent neural networks with discontinuous activations and periodic coefficients or constant coefficients, respectively. Finally, we give one numerical example to demonstrate the effectiveness of the derived theoretical results.

Finite-time coordination of a class of second-order nonlinear multi-agent systems

The authors study the second-order finite-time coordination problems of nonlinear multi-agent systems with directed graph. By using the homogeneous theories, we firstly give a finite-time coordination controller for the leaderless multi-agent system. Then, another finite-time controller for leader-follower multiagent system was given. Finally, the authors give a simulation, which shows the effectiveness of the given finite-time coordination controllers.

Applications of adaptive variable step-size algorithm in turbulence observation system

In turbulence observation system, noise signal is random and difficult to identify, which will pollute the real signal and affect the quality of the data. To eliminate the noise signal, the article puts forward a kind of adaptive variable step-size de-noising algorithm. Firstly, raw data is changed into corresponding physical parameters, and spectral analysis is used to analyze the relationship among these parameters, and then, according to the correlation to construct the variable step-size de-noising algorithm, and through error to adjust shape of the step size factor to control the optimal weight coefficient. Finally, simulation and observation data is used to verify the effectiveness of the algorithm, and Goodman’s filter algorithm is compared with the algorithm. The results show that the algorithm has higher precision and the noise is effectively reduced. c ©2016 All rights reserved.