Robust constrained model predictive control of piecewise linear systems with bounded additive disturbances

This paper provides a solution to the problem of robust model predictive control (MPC) for piecewise linear (PWL) systems with constraints and persistent, unknown but bounded disturbances. The robust MPC policy is to minimize a quadratic performance index with terminal cost for the nominal PWL systems and with tightened systems constraints and tightened terminal set constraints for all admissible disturbances. Off-line, pre-determined feedback gains for PWL systems are introduced and are applied to generate a candidate correction policy to show how constraints in the MPC optimization are restricted against persistent bounded disturbances. On-line, at each sampling time, the resultant optimization problem is a mixed integer quadratic programming (MIQP) of similar complexity to that required in MPC of nominal PWL systems. The robust predictive controller obtained in this way guarantees robust feasibility, constraints satisfaction and robust convergence for all admissible disturbances. Simulation results demonstrate the effectiveness of the proposed approach.