Detector-based boundary synchronization control of hidden Markov jump reaction–diffusion neural networks

This paper addresses the passive synchronization control problem for continuous-time hidden Markov jump reaction–diffusion neural networks via a detector-based boundary control method. The abrupt variations in parameters and structure in networks are modeled as a hidden Markov jump model encompassing the hidden state and the observed state. The model relaxes the assumption of fully observable states in a Markov process by estimating the hidden states using a detector. A distinctive feature of this model is that it comprises different detection information, such as complete information, no information, and others, enabling us to observe in a general manner. On the basis of the states estimated by the detector, a mode-dependent boundary synchronization controller subject to Neumann boundary conditions is proposed. Compared with existing full-domain controller design methods, this controller reduces the number of controllers, thereby lowering costs. By solving convex optimization problems, sufficient conditions for ensuring the stability and expected passive performance of the systems are deduced, and the gains of the desired controller are obtained. Finally, the correctness and superiority of the proposed method are validated through comparative examples.