Synchronization of multiple reaction–diffusion memristive neural networks with known or unknown parameters and switching topologies

Abstract

This paper investigates the synchronization problems of multiple reaction–diffusion memristive neural networks (MRDMNNs) with known or unknown parameters and switching topologies via distributed control. In complex environment, the proposed system may face switching topologies, diffusion effects, external disturbance, parameter mismatch or uncertainty, so designing security control laws to synchronize the proposed system is a enormous challenge. The parameter mismatch terms herein are extended to be unbounded, which is different from the general boundedness hypothesis. Since the parameter mismatch term would be known or unknown, we design a novel parameter-dependent controller for the known condition and a novel parameter-independent adaptive controller for the unknown condition respectively. By constructing new Lyapunov functions, using some properties of M-matrix and robust control method, the synchronization errors will all converge into a bound set via the two designed nonlinear controllers. And we are able to select appropriate control parameters to control the upper bound. Moreover, the obtained theorems can determine the feedback control gains, which can be used for security control. Finally, two numerical simulations are given to support the obtained theoretical results.