Control of discrete-time piecewise affine systems

Abstract: In this paper we propose a new approach for the control of discrete-time piecewise affine hybrid systems on full-dimensional polytopes. The new strategy is divided into a local and a supervisory control problem. The local problem is to reach and cross one facet of a polytope ensuring that the next sample of the time-discrete trajectory is picked up in the adjacent polytope. Therefore, a local piecewise affine control law is obtained by solving an optimization problem, minimizing the retention period of the trajectory in the polytope or the quadratic sum of the input signal. This procedure is based on system inherent bounds. The supervisory control problem is to find a suitable combination of polytopes and local control strategies that transfers the trajectory to the operating point and keeps it there. Copyright c©2005 IFA