Implementable Receding Horizon Control for Constrained Systems

Abstract

In this paper, new state feedback and output feedback receding horizon controllers, based on a finite input and state horizon cost with a finite terminal weighting matrix, are proposed for discrete linear systems with input and state constraints. We propose matrix inequality conditions on the terminal weighting matrix under which closed loop exponential stability is guaranteed for both cases of state feedback and output feedback. We show that such a terminal weighting matrix can be obtained by solving an LMI (Linear Matrix Inequality). An artificial invariant ellipsoid constraint is introduced in order to relax the conventional terminal equality constraint and to handle constraints. Using the invariant ellipsoid constraints, a feasibility condition of the optimization problem is presented and a region of attraction is characterized for constrained systems with the proposed receding horizon control. A couple of illustrative examples are included.