Controller complexity reduction for piecewise affine systems through safe region elimination

We consider the class of piecewise affine optimal state feedback control laws applied to discrete-time piecewise affine systems, motivated by recent work on the computation of closed-form MPC controllers. The storage demand and complexity of these optimal closed-form solutions limit their applicability in most real-life situations. In this paper we present a novel algorithm to a posteriori reduce the storage demand and complexity of the closed-form controller without losing closed-loop stability or all time feasibility while guaranteeing a bounded performance decay compared to the optimal solution. The algorithm combines simple polyhedral manipulations with (multi-parametric) linear programming and the effectiveness of the algorithm is demonstrated on a large numerical example.