Model predictive control for continuous-time piecewise affine systems based on mode controllability

This paper presents an approximate semi-offline approach to model predictive control of continuous-time piecewise affine (CTPWA) systems. The proposed method computes in the offline phase a controllable set and a minimum transition cost associated with each discrete state sequence. Then at each sampling time in the online phase, the controller determines the optimal sequence of intermediate target states over a prediction horizon, taking advantage of the information precomputed off line. By effectively distributing the computation over the offline phase and the online phase, real-time control is achieved, striking a good balance between the amount of precomputed data and the online computation time. The proposed method has been applied to a simple CTPWA system, obtained by piecewise linear approximation of a pendulum.