Pinning control and adaptive control for synchronization of linearly coupled reaction‐diffusion neural networks with mixed delays

Abstract

SummaryThis paper focuses on the pinning control and adaptive control for synchronization of an array of linearly coupled reaction‐diffusion neural networks with mixed delays (that is, discrete and infinite distributed delays) and Dirichlet boundary condition. Firstly, the asymptotical synchronization of coupled semilinear diffusion partial differential equations with mixed time delays is achieved by employing pinning control scheme. The pinning controller is obtained by using Lyapunov‐Krasovskii functional stability theory. The stability condition is represented by linear matrix inequality. The controller gain matrix is easy to be solved. Secondly, the adaptive synchronization condition of an array of linearly coupled reaction‐diffusion neural networks with mixed delays is obtained by using adaptive control scheme. Finally, two numerical examples of coupled semilinear diffusion partial differential equations with mixed time delays are given to illustrate the correctness of the obtained results.

Chaos control and circuit implementation of a class of double‐wing chaotic system

“…Thereafter, many researchers have completed a lot of research on chaos control in different fields and have published many successful experimental reports in nonlinear field. () Many chaos control schemes have been proposed in recent years,() such as robust control,() feedback control,() adaptive control,() backstepping control,() sliding mode control,() neural network control, fuzzy logic control,() and optimal control. ()…”

Robust adaptive synchronization of complex network with bounded disturbances

“…Adaptive pinning impulsive synchronization was investigated for time-delayed complex networks [30]. An adaptive pinning synchronization criterion was obtained for linearly coupled reaction-diffusion neural networks with mixed delays [31].…”

Adaptive Aperiodically Intermittent Synchronization for Complex Dynamical Network with Unknown Time-Varying Outer Coupling Strengths

“…Researchers were mainly concerned with the issues of modelling, properties analysis, dynamical evolution, and synchronization control of complex dynamical networks. Among these issues involved, synchronization is one of the most interesting topics and has been extensively investigated [1][2][3][4][5][6][7][8][9][10][11][12]. There are mainly two kinds of strategies for synchronization of complex dynamical networks: one is to improve the network synchronization capability by changing the properties of the network itself, such as topology structure and coupling strengths.…”

“…There are mainly two kinds of strategies for synchronization of complex dynamical networks: one is to improve the network synchronization capability by changing the properties of the network itself, such as topology structure and coupling strengths. The other is to act on the network with external control injection, which is a representative of control theory, mainly including variable feedback control method, pinning control method [2,4], adaptive control method [5], event-triggered control [8], impulse control method, intermittent pinning control [9], and slide mode control method [10,11].…”