Input-to-state stability of robust receding horizon control with an expected value cost

This paper is concerned with the control of constrained linear discrete-time systems subject to bounded state disturbances and arbitrary convex state and input constraints. The paper employs a class of finite horizon feedback control policies parameterized as affine functions of the system state, calculation of which has recently been shown to be tractable via a convex reparameterization. When minimizing the expected value of a finite horizon quadratic cost, we show that the value function in this finite horizon control problem is convex. When policies of this type are used in the synthesis of a robust receding horizon controller, we provide sufficient conditions under which the closed-loop system is input-to-state stable (ISS).