Abstract
This paper employs the Input-to-State Stability (ISS) framework to investigate the robustness of discrete-time Piece-Wise Affine (PWA) systems in closed-loop with Model Predictive Controllers (MPC), or hybrid MPC for short. We show via an example taken from literature that stabilizing hybrid MPC can generate MPC values functions that are not ISS Lyapunov functions for arbitrarily small additive disturbances. As a consequence, it is not easy to prove that nominally stabilizing hybrid MPC schemes are robust. This motivates the need to design MPC schemes for hybrid systems with an a priori robust stability guarantee. A possible solution to this problem was recently developed by the authors for a particular class of PWA systems, i.e. when the origin lies in the interior of one of the regions in the partition. The main contribution of this paper is a novel dual-mode MPC algorithm for hybrid systems with an a priori ISS guarantee. This MPC scheme is applicable to general PWA systems, i.e. when the origin may lie on the boundaries of multiple regions in the partition.
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