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.
