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DES abstractions for the supervisory control of hybrid systems

¹ Department of Engineering, LeTourneau University, Longview, TX, USA
² Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, USA

^* To whom correspondence should be addressed. E-mail: marianiordache{at}letu.edu.

	Abstract

An examination of the literature results on timed and untimed discrete event system (DES) models reveals clearly that the supervisory control problem is more tractable on untimed models. Thus it is interesting to consider the extent to which untimed DES models can be used to design controllers for dynamical systems. In order to approach a larger class of systems appropriate abstraction methods are necessary as well as some extensions of the untimed supervisory control methods. This paper proposes an abstraction procedure that can be used to extract untimed DES models from hybrid automata models with control inputs and continuous disturbances. The abstractions obtained using this procedure are state machines in which every state corresponds to a region of the state space of the hybrid automaton and transitions between states correspond to transitions between the regions. Results describing properties of the abstraction procedure are obtained, including a semidecidability result. The procedure is useful not only for sequential problems, but also in the context of concurrency.

First published on September 7, 2009
Transactions of the Institute of Measurement and Control 2009, doi:10.1177/0142331208097839


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