Approximate min-max MPC for linear hybrid systems

This paper presents a Receding Horizon Control (RHC) strategy to robustly control linear hybrid systems subject to bounded additive disturbances. First, the open-loop finite horizon min-max optimal control problem associated with the RHC strategy is presented, defining a mixed-integer optimization problem. The goal of the min-max formulation is to minimize the worst-case cost of the performance index, while guaranteeing performance/safety constraints for all possible disturbance realizations. Then it will be proved that feasibility at the initial time as well as convexity arguments and set-invariance assumptions are sufficient conditions to guarantee robust stability and performance of the closed-loop system. Simulation results for a perturbed hybrid system will demonstrate the potential of the proposedrobust optimal control design.