A control strategy for control of discrete-time piecewise affine systems on polytopes using system inherent bounds

In this paper we propose a local control strategy for the control of discrete-time piecewise affine systems on full-dimensional polytopes using system inherent hounds. The overall control strategy is divided into this local control and a supervisory control. The local control problem is to reach and cross one selected facet of a polytope ensuring that the next sample of the discrete-time trajectory is picked up in the adjacent polytope. The procedure is based on system inherent bounds assisted by conditions for the discrete-time gradient of the system. The controller design can be performed intuitively or with both the inherent bounds and the conditions an optimization problem can be formulated minimizing a performance index. A control law is obtained that is valid on the entire polytope for one specific facet. The supervisory control problem is to find a suitable combination of polytopes and local control strategies that transfer the trajectory to the polytope that contains the operating point.