Adaptive tracking synchronization for coupled reaction–diffusion neural networks with parameter mismatches

Abstract

In this paper, tracking synchronization for coupled reaction–diffusion neural networks with parameter mismatches is investigated. For such a networked control system, only local neighbor information is used to compensate the mismatch characteristic termed as parameter mismatch, uncertainty or external disturbance. Different from the general boundedness hypothesis, the parameter mismatches are permitted to be unbounded. For the known parameter mismatches, parameter-dependent controller and parameter-independent adaptive controller are respectively designed. While for fully unknown network parameters and parameter mismatches, a distributed adaptive controller is proposed. By means of partial differential equation theories and differential inequality techniques, the tracking synchronization errors driven by these nonlinear controllers are proved to be uniformly ultimately bounded and exponentially convergent to some adjustable bounded domains. Finally, three numerical examples are given to test the effectiveness of the proposed controllers.