Necessary and Sufficient Conditions for Constraint Satisfaction in Switched Systems using Switch-Robust Control Invariant Sets

This paper studies the control of constrained systems whose dynamics and constraints switch between a finite set of modes over time according to an exogenous input signal. We define a new type of controlinvariant sets for switched constrained systems, called switch-robust control invariant (switch-RCI) sets, that are robust to unknown mode switching and exploit available information on minimum dwell-time and admissible mode transitions. These switch-RCI sets are used to derive novel necessary and sufficient conditions for the existence of a control-law that guarantees constraint satisfaction in the presence of unknown mode switching with known minimum dwell-time. The switch-RCI sets are also used to design a recursively feasible model predictive controller (MPC) that enforces closed-loop constraint satisfaction for switched constrained systems. We show that our controller is non-conservative in the sense that it enforces constraints on the largest possible domain i.e. constraints can be recursively satisfied if and only if our controller is feasible. The MPC and switch-RCI sets are demonstrated on a vehicle lane-changing case study.