A necessary and sufficient RHC stabilizability condition for stochastic control with delayed input

摘要

We study the mean-square stabilizability of Itô stochastic systems with delayed input. In contrast to most previous results, where only sufficient condition was derived, this paper proposes a necessary and sufficient stabilization condition by exploring the receding horizon control (RHC) and the coupled Riccati equations. It is shown that the system controlled by RHC is stabilizable if and only if the two coupled Lyapunov type inequalities are satisfied. The key is to design a novel cost function based on the optimal cost of finite horizon optimization problem.