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

This paper is concerned with the stability of a class of receding horizon control (RHC) laws for constrained linear discrete-time systems subject to bounded state disturbances and convex state and input constraints. The paper considers the class of finite horizon feedback control policies parameterized as affine functions of the system state, calculation of which can be 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 is convex. When solving this optimal control problem at each time step and implementing the result in a receding horizon fashion, we provide sufficient conditions under which the closed-loop system is input-to-state stable (ISS). (c) 2007 Elsevier Ltd. All rights reserved.