Online Data-Driven Model Predictive Control for Switched Linear Systems

In this article, we consider the stabilization problem of switched systems consisting of a limited number of unknown linear subsystems regulated by unknown switching signals. To this end, we first develop a data-driven model predictive control (MPC) scheme with the online input–output trajectory of switched linear systems. Considering the mismatch of the data during the switching interval, the slack variable is introduced to ensure the feasibility of the algorithm. Then, the stability of the switched linear system is analyzed theoretically. The exponential stability of one single subsystem is shown with the existence of the artificial perturbation in the actual control input. We also elucidate the uniformly bounded growth of the system trajectory over the switching interval. Based on these results, we prove that the closed-loop system is exponentially stable, provided the switching signal satisfies the dwell-time condition. Finally, the effectiveness of the control law is demonstrated with the numerical simulation of the aero-engine corrected speed control under different flight conditions.