Optimal control and stabilization for discrete‐time networked control systems with multichannel Markovian packet losses

Abstract

This article is concerned with the optimal control and stabilization for the discrete‐time networked control systems with Markovian fading channels in a diagonal form, which indicates that different channel possesses different correlated fading property. To overcome the essential difficulty resulting from the multi communication channel packet losses and the correlation of the Markov chain, a new multistate Markov chain is introduced, by which the optimal control and stabilization for the NCSs with the diagonal form of Markovian fading channels are transformed into the ones for the general Markovian jump linear system. According to the converted system, a new modified maximum principle is presented, that is, a forward‐backward stochastic difference equation (FBSDE) is obtained. In the finite horizon design, the key step is to seek for the relationship between the system state and optimal costate. By the obtained relation and based on a new coupled difference Riccati equation (CDRE), a necessary and sufficient solvability condition for the optimal control is obtained as well as an explicit expression for the optimal controller. For the infinite horizon case, a new type of coupled Lyapunov function is defined, which keeps consistent with the finite horizon optimal performance index. By introducing a new coupled algebraic Riccati equation and using the defined Lyapunov function, a necessary and sufficient stabilization condition in the mean‐square sense and an infinite horizon optimal controller are presented. Finally, a numerical example is supplied to illustrate the efficiency of the proposed results.