Stabilization of sampled-data nonlinear systems by receding horizon control via discrete-time approximations

Results on stabilizing receding horizon control of sampled-data nonlinear systems via their approximate discrete-time models are presented. The proposed receding horizon control is based on the solution of Bolza-type optimal control problems for the parametrized family of approximate discrete-time models. This paper investigates both situations when the sampling period T is fixed and the integration parameter h used in obtaining approximate model can be chosen arbitrarily small, and when these two parameters coincide but they can be adjusted arbitrary. Sufficient conditions are established which guarantee that the controller that renders the origin to be asymptotically stable for the approximate model also stabilizes the exact discrete-time model for sufficiently small integration and/or sampling parameters.