Discrete Supervisory Control of Hybrid Systems Based on l-Complete Approximations

Authors:
Thomas Moor;Jörg Raisch;Siu O’Young
Affiliations:
Research School of Information Sciences and Engineering, Australian National University, Canberra ACT 0200, Australia thomas.moor@anu.edu.au;Max-Planck-Institut für Dynamik komplexer technischer Systeme, D-39106 Magdeburg, Federal Republic of Germany raisch@mpi-magdeburg.mpg.de;Memorial University of Newfoundland, St. John’s, Newfoundland, Canada A1B 3X5 oyoung@engr.mun.ca
Venue:
Discrete Event Dynamic Systems
Year:
2002

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Abstract

The topic of this paper is the synthesis of discrete supervisory control for hybrid systems \Sigma with discrete external signals. Such systems are in general neither l-complete nor can they be represented by finite state machines. Our solution to the control problem is as follows: we find the strongest l-complete approximation (abstraction) \Sigma_l for \Sigma, represent it by a finite state machine, and investigate the control problem for the approximation. If a solution exists on the approximation level, we synthesize the maximally permissive supervisor for \Sigma_l. We show that it also solves the control problem for the underlying hybrid system \Sigma. If no solution exists, approximation accuracy can be increased by computing the strongest k-complete abstraction \Sigma_k, k l. The basic ideas regarding the approximation step are explained within the framework of Willems’ behavioral systems theory. Implementation issues are treated in a state space framework, and the main results are interpreted from a traditional control engineering point of view.