Characterization of switching sequences on system with dwell-time restriction for Model Predictive Control

This work proposes a Model Predictive Control (MPC) approach for a switching discrete-time linear system where the switching signal is prescribed but its future values are unknown except that at the current time. The switching signal satisfies a minimal dwell time restriction of τ steps between successive switchings (including the case of τ = 1) 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. These include the use of a modified returnable set as the terminal constraint; the introduction of consistency constraints on the predicted controls for recursive feasibility consideration; a min-max optimization criterion as the cost function; the splitting of the horizon length into two portions for recursive feasibility consideration and exponential stability of the closed-loop system. The proposed approach is demonstrated by numerical example.