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DES Abstractions for the Supervisory Control of Hybrid Systems Marian V. Iordache

Summary: DES Abstractions for the Supervisory Control of Hybrid Systems
Marian V. Iordache
and Panos J. Antsaklis
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.
1 Introduction
Numerous methods have been proposed for the supervisory control of discrete event systems (DESs). Since
a DES model is usually not a complete model of a plant, it is important to ensure that it is obtained in such
a way that any controller designed based on the DES model will be able to satisfy the specifications when
in closed-loop with the actual plant. Plants modeled by DESs are often more accurately modeled by hybrid


Source: Antsaklis, Panos - Department of Electrical Engineering, University of Notre Dame


Collections: Engineering