On the Stability of a Class of Robust Receding Horizon Control Laws for Constrained Systems

This paper is concerned with the stability of a class of robust and constrained optimal control laws for linear discrete-time systems subject to bounded state disturbances and arbitrary convex constraints on the states and inputs. The paper considers the class of feedback control policies parameterized as affine functions of the system state, calculation of which has recently been shown to be tractable via a suitable convex reparameterization. When minimizing the expected value of a quadratic cost, we show that the resulting value function in the optimal control problem is convex. When used in the design of a robust receding horizon controller, we provide sufficient conditions to establish that the closed-loop system is inputto-state stable (ISS). The paper further shows that the resulting control law has an interesting interpretation as the projection of the optimal unconstrained linearquadratic control law onto the set of constraint-admissible control policies.