Model Predictive Control for Switching Systems With Dwell-Time Restriction

This work proposes a model predictive control (MPC) approach for a switching linear system where the switching signal is prescribed with unknown future values. The switching signal is known only at its current value, satisfies a minimal dwell-time restriction of
$\tau$
steps between successive switchings and is otherwise arbitrary. Under such a setting, the MPC optimization problem has to allow for all admissible switching sequences within a given horizon length. Such a formulation necessitates several other features: the use of a modified returnable set as the terminal constraint; the introduction of consistency constraints on the predicted controls; a min-max optimization criterion as the cost function; the splitting of the horizon into two portions for recursive feasibility consideration and exponential stability of the closed-loop system. The proposed approach is demonstrated by a numerical example.