Multiple prediction trajectories in MPC for PWA systems

In this paper, a Model Predictive Control problem for constraint discrete time Piecewise Affine (PWA) systems based on quadratic performance criteria is considered. The number of possible switching sequences in PWA systems grows exponentially with the length of the optimal control problem horizon that leads to multiple trajectories in the receding horizon strategy, and should be considered in calculating the optimal input signal at each step. Firstly, the number of possible trajectories is reduced by introducing two new concepts; minimum dwell sample and maximal reachable area, without loss of optimality. Secondly, using the minimum dwell sample notion, a new suboptimal solution is proposed to reduce the number of possible prediction trajectories. Finally, the effectiveness of the proposed method is shown through simulation results.