Predictive Control of Hybrid Systems: Stability Results for Sub-Optimal Solutions

This article presents a novel model predictive control (MPC) scheme that achieves input-to-state stabilization of constrained discontinuous nonlinear and hybrid systems. Input-tostate stability (ISS) is guaranteed when an optimal solution of the MPC optimization problem is attained. Special attention is paid to the effect that sub-optimal solutions have on ISS of the closed-loop system. This issue is of interest as firstly, the infimum of MPC optimization problems does not have to be attained and secondly, numerical solvers usually provide only sub-optimal solutions. An explicit relation is established between the deviation of the predictive control law from the optimum (called the optimality margin) and the resulting deterioration of the ISS property of the closed-loop system (called the ISS margin).