Set invariance under controlled nonlinear dynamics with application to robust RH control

This paper is concerned with the characterization of the maximal admissible uncertainty under which a nonlinear discrete-time dynamic system can be stabilized in the neighborhood of the origin by a Receding Horizon (RH) state-feedback control scheme. This topic is of great interest in both analysis and design of robust RH controllers for constrained discrete-time nonlinear systems. In particular, under mild assumptions on the nominal transition map, the robustness of the overall RH control scheme is shown to depend on the invariance properties of the terminal set constraint, which is a design parameter for the controller. In this framework, resorting to set invariance theoretic arguments, a numerical procedure is proposed which allows to evaluate the robust invariance properties of the terminal set constraint. An application example is provided to show the effectiveness of the proposed approach.