RECEDING HORIZON CONTROL AND DISCONTINUOUS STATE-FEEDBACK STABILIZATION

This paper addresses three aspects of receding horizon control in disc rete-time: (1) feedback stabilization of general nonlinear systems wit h receding horizon control; (2) the generation of stabilizing feedback control laws that are discontinuous in the state; and (3) the suitabi lity of receding horizon control to stabilize feedback-linearizable sy stems. The nonlinear receding horizon controller is shown via a Lyapun ov function argument to be asymptotically stabilizing for a large clas s of nonlinear systems. As a special case, nonlinear systems that can be locally feedback linearized can be locally asymptotically stabilize d with nonlinear receding horizon control. A simple example shows that there exist controllable nonlinear discrete-time systems that cannot be asymptotically stabilized with continuous feedback. For this exampl e, the nonlinear receding horizon controller generates an asymptotical ly stabilizing feedback law. The discontinuity in the resulting feedba ck law is discussed and numerical results are provided.