Control of Piecewise-Affine Hybrid Systems - Extended abstract

The character of this paper is an extended abstract of the approach developed by the authors for control of piecewise-affine hybrid systems. Control of hybrid systems is a wide ranging research topic with many theoretical problems. The authors have therefore decided early on to restrict attention to piecewise-affine hybrid systems on polytopes. The approach developed includes for affine systems on polytopes sufficient conditions for the problems (1) leaving the polytope in finite time through a prespecified set of facets; (2) remaining inside a particular polytope forever; and (3) converging to a fixed state inside a particular polytope. For piecewise-affine hybrid system on polytopes a procedure for reachability and control synthesis is proposed consisting of (1) for each discrete state the computation of all possible exit facets and exit events; (2) abstraction of the continuous dynamics to an automaton; and (3) the search of a path in the automaton from an initial discrete state to a target discrete state. Open research issues for control of hybrid systems are stated.