Stabilizing model predictive control scheme for piecewise affine systems with maximal positively invariant terminal set

An efficient algorithm is proposed for computing the solution to the constrained finite time optimal control (CFTOC) problem for discrete-time piecewise affine (PWA) systems with a quadratic performance index. The maximal positively invariant terminal set, which is feasible and invariant with respect to a feedback control law, is computed as terminal target set and an associated Lyapunov function is chosen as terminal cost. The combination of these two components guarantees constraint satisfaction and closed-loop stability for all time. The proposed algorithm combines a dynamic programming strategy with a multi-parametric quadratic programming solver and basic polyhedral manipulation. A numerical example shows that a larger stabilizable set of states can be obtained by the proposed algorithm than precious work.