A Computationally Efficient Trajectory Prediction in MPC for Piecewise Affine Systems

A novel model predictive control strategy is proposed to determine an optimal control signal which steers the states of a constraint piecewise affine system to a desired target point through suboptimal state trajectories, based on quadratic performance criteria. In piecewise affine systems, the number of possible switching sequences grows exponentially with the length of the prediction horizon that leads to multiple trajectories in the receding horizon strategy; and should be considered in calculating the optimal control signal at each step. The proposed method is an optimal solution in terms of continuous variables with obtained suboptimal switching sequence. At each sample time, this method restricts the number of necessary Quadratic Programming (QP) problems to the length of the prediction horizon by dividing the optimization problem into sub-problems through introducing a new concept, minimum dwell sample. A local control horizon concept is also introduced to reduce the length of the optimization vector and a mode avoidance technique is proposed to deal with piecewise affine systems that have some uncontrollable or undesired modes in state space. This technique relaxes the full mode controllability assumption of the system using an artificial target to avoid uncontrollable modes. The convergence and feasibility of the method are proven and the effectiveness of the proposed approach is demonstrated by simulation results.