Optimal control of linear systems with stochastic parameters for variance suppression

In this paper, we consider an optimal control problem for a linear discrete time system with stochastic parameters in the infinite time horizon case. This paper focuses on optimal control for systems with stochastic parameters whereas the traditional stochastic optimal control theory mainly considers systems with deterministic parameters with stochastic noises. This paper extends the authors' former result on the same subject in the finite time horizon case to the infinite time horizon case. The main result is to provide a feedback controller suppressing the variation of the state and to prove stochastic stability of the corresponding feedback system by taking care of both the average and the variance of the state transient. Furthermore, a numerical simulations demonstrate the effectiveness of the proposed method.