Explicit model predictive control for multi-rate piecewise linear systems

This paper studies the explicit model predictive control for piecewise linear (PWL) systems with the output sampling period several times larger than the input updating period. First, based on dynamic programming, the model predictive control optimization problem is decomposed into multi-stage optimization problems with one-step optimal horizon. Further, optimization problem of each stage is separated into sub-problems according to the sub-models of the piecewise linear system and the form of objective function. After that, by utilizing multi-parametric quadratic programming (MP-QP) technique and comparing the solutions of all the sub-problems, the optimal explicit control laws are obtained. Besides, the maximal positively invariant set of the piecewise linear system is chosen as the terminal constraint set of the optimization problem such that the stability can be ensured. The numerical example shows that the proposed explicit model predictive control can reduce online computation and satisfy the demand of the multi-rate piecewise linear system with fast updating speed of input. Copyright © 2013 Acta Automatica Sinica. All rights reserved.