Control of Discrete-Time Piecewise Affine Systems

In this paper we propose a new approach for the control of discrete-timepiecewise affine hybrid systems on full-dimensional polytopes. The newstrategy is divided into a local and a supervisory control problem. The localproblem is to reach and cross one facet of a polytope ensuring that the nextsample of the time-discrete trajectory is picked up in the adjacent polytope.Therefore, a local piecewise affine control law is obtained by solving anoptimization problem, minimizing the retention period of the trajectory in thepolytope or the quadratic sum of the input signal. This procedure is based onsystem inherent bounds. The supervisory control problem is to find a suitablecombination of polytopes and local control strategies that transfers thetrajectory to the operating point and keeps it there.