Infinite‐horizon optimal control for networked control systems with Markovian packet losses

This article is concerned with the infinite‐horizon optimal control for networked control systems with Markovian packet losses. We focus on the case that packet losses may occur in an unreliable communication channel between the sensor and the controller. This sort of packet loss enables the optimal control problem to fall into the category of optimal output‐feedback control. Also, the output involves multiplicative noise. As well known, the separation principle fails to hold in a multiplicative‐noise setting. Thus the problem is very involved. By solving forward and backward stochastic difference equations and making convergence analysis, we acquire the necessary and sufficient solvability condition and the explicit optimal controller. The achieved results are illustrated by numerical examples.