An Efficient and Stabilizing Model Predictive Control of Switched Systems

Model Predictive Control (MPC) of switched systems typically requires an on-line solution of a Mixed Integer Program (MIP). Since the worst case complexity of the optimization problem increases exponentially with respect to the number of integer variables, an on-line implementation of the MPC for problems with large number of sub-systems and/or large horizons is usually expensive. In this technical note, we propose a stabilizing MPC formulation for state-dependent switched systems, that enables a tradeoff between the computational complexity of the MPC controller and the optimal performance of the closed-loop system. The proposed approach uses a pre-terminal set, in addition to the positively invariant terminal set, which aids in reducing the on-line complexity although at the expense of optimality. Examples are presented to illustrate the computational benefits of the proposed MPC strategy over existing MPC for switched systems.