Robust Predictive Control for Constrained Uncertain Piecewise Linear Systems using Linear Matrix Inequalities

This paper considers discrete-time, uncertain Piecewise Linear (PWL) systems affected by polytopic parameter variations. Classical robust controller for uncertain PWL systems is known to be a complex problem, where the on-line computation becomes computationally burdensome and inapplicable. In this paper we present a new technique to solve robust constrained infinite horizon model predictive control for uncertain PWL systems using Linear Matrix Inequalities (LMI). The controller objective is to regulate the system states to a constant set-point that could be in general different from the origin, despite the uncertainties. Constraints over the control and output signals are taken into account. The proposed controller guarantees the system stability and reduces the computation load. To further reduce the computation load, an algorithm to calculate off-line solutions based on the system state location is proposed; where a pre-computed state-feedback control law is applied once the system states enter the region of PWL system containing the shifted origin. This algorithm reduces considerably the computation time while offering a suboptimal solution. A numerical example to validate the efficiency of the developed techniques is presented.