A dual-terminal set based robust tube MPC for switched systems

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This article considers the robust regulation problem for a class of constrained linear switched systems with bounded additive disturbances. The proposed solution extends the existing robust tube based model predictive control (RTBMPC) strategy for non-switched linear systems to switched systems. RTBMPC utilizes nominal model predictions, together with tightened sets of state and input constraints, to obtain a control policy that guarantees robust stabilization of the dynamic systems in presence of bounded uncertainties. Similar to RTBMPC for non-switched systems, a disturbance rejection proportional controller is used to ensure that the closed loop trajectories of the switched linear system are bounded in a tube centered on the nominal system. To account for the switching dynamics, the gain of this controller is chosen to simultaneously stabilize all switching dynamics. The RTBMPC for the switched system requires an on-line solution of a Mixed Integer Quadratic Program (MIQP). To reduce the complexity of the MIQP, a sub-optimal design is proposed, which considers the notion of a pre-terminal set in addition to the usual terminal set used to ensure stability. The RTBMPC design with the pre-terminal set aids in tuning the trade-off between the complexity of the control algorithm with the optimal performance of the closed-loop system while ensuring robust stability. Examples are presented to illustrate features of the proposed MPC.