EU ESPRIT-LTR Project (26270) Verification of Hybrid Systems (VHS) Control of Piecewise-Linear Hybrid Systems Intermediate Report

The purpose of this report is to present research results on control of piecewise-linear hybrid systems of an investigation carried out as part of the project Verification of Hybrid Systems (VHS). Many engineering systems can in a first approximation be described by a piecewise-linear hybrid system. Moreover, the computational and complexity issues of this class of systems seems comparatively simple. Therefore this class deserves attention for the development of control theory. E.D. Sontag has introduced the class of piecewise-linear systems in a paper published in 1981, see [48]. A subclass of this class forms the piecewise-linear hybrid systems as defined elsewhere in this report, see [50]. Hybrid systems have been considered since the 1980’s, see [14] for references and [55] for a definition. Piecewise-linear hybrid systems are, in regard to the geometry of the spaces, based on polyhedral sets. The fact that polyhedral sets can be described by finite-dimensional parameters, makes these sets a suitable class of objects for control and system theory of hybrid systems. Thus the class of piecewise-linear hybrid systems seems very useful for modelling of engineering systems and because of its mathematical properties. About control synthesis for hybrid systems has been written by many researchers, in particular by those of the research group of Shankar Sastry at the University of California at Berkeley. Yet it is fair to say that the current status of control theory for hybrid systems is far from satisfactory. No