An Algorithm for the Generation of Control Laws for Linear Hybrid Systems

In [TE93] the authors discussed the notion of controllability of hybrid systems in connection with a framework for the speci cation of hybrid systems that is based on the hybrid automata proposed by [ACHH93], and presented an algorithm to generate correct controllaws for such systems. This report should be seen as a complement to the above mentioned paper in that it describes and proves the introduced algorithm. We assume the reader to be familiar with the concepts of jump-room, extended jump-room, phase-transition, : : : , which are described in [TE93]. In this report the program-package Hybrid (implemented in MATLAB code) is introduced and the underlying ideas and concepts are discussed. The program's purpose is to determine whether or not a hybrid system A, speci ed by the seven-tuple A = (VD; Q; s1; s2; 1; 2; 3), can be controlled to have an acceptable run that takes A from its initial state s1 to its nal state s2. In addition, a set of control-laws can be synthesized for the execution of an acceptable run, if there exists one.