Optimal Control and Stabilization for NCS over Multi-Hop Relay Networks

This paper is concerned with the optimal control for networked control systems over multi-hop relay networks. In the transmission process, there exist package losses which lead to heavy damage. To overcome the multi-hop relay package losses, we introduce the relay code and a new Markov chain which convert the optimal control with series of packet losses into the general Markovian jumping parameter system. Based on the converted system, a modified maximum principle is developed, which is actually a forward-backward jumping parameter difference equation. In the finite horizon, the key step is to reveal the relationship between the system state and optimal costate. The optimal controller as well as the optimal performance is deduced via the solutions to the optimal costate and one type of coupled difference Riccati equation. In the infinite horizon, a new type of Lyapunov function is defined, by which a necessary and sufficient stabilization condition is obtained, and an infinite optimal controller is developed.