Abstract:

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.

Key words: constrained optimal predictive control, multi-parametric quadratic programming, dynamic programming, receding horizon control, positively invariant set