State Feedback Policies for Robust Receding Horizon Control: Uniqueness, Continuity, and Stability

In this paper we consider the problem of controling linear discrete-time systems subject to unknown disturbances and mixed constraints on the states and inputs, using a class of affine state-feedback control policies implemented in a receding horizon fashion. By defining a quadratic cost function in the disturbance-free sequence of states and controls, we demonstrate that this parameterization can be used in the synthesis of a nonlinear time-invariant receding horizon control law that is robustly invariant, unique and continuous in the initial state, and with guaranteed input-to-state (ISS) stability. Our method relies in part on the exploitation of an equivalent control policy parameterized as an affine function of the past disturbance sequence, and we show that this parameterization has the added benefit of enabling calculation of the control law at each stage using a single tractable quadratic program (QP) when the disturbance set is a polytope or affine map of a 1- or ∞-norm bounded set.