Multiparametric predictive control for a class of Discrete Event Systems

Abstract

The focus of this paper is to synthesise an optimal control law that allows to track a desired trajectory with respect to the constraints both on the control and state vectors for a class of Discrete Event Systems (DESs). For this, a geometric approach of a model predictive control is extended to a class of DESs modelled by P-time event graphs in the standard algebra using the dater equations. The use of the concept of (A, B)-invariance allows us to obtain the polyhedral parametric constraints. The constrained parametric model predictive control leads for a multiparametric quadratic programming (MP-QP) for which the solution is a feedback Piece-Wise Affine (PWA) control defined for different feasible regions.