Supervision of infinite behavior of discrete-event systems
Some basic results of supervisory control theory are extended to the setting of $\omega $-languages, formal languages consisting of infinite strings. The extension permits the investigation of both liveness and safety issues in the control of discrete-event systems. A new controllability property ap...
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| Veröffentlicht in: | SIAM journal on control and optimization 1994-07, Vol.32 (4), p.1098-1113 |
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| container_title | SIAM journal on control and optimization |
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| creator | THISTLE, J. G WONHAM, W. M |
| description | Some basic results of supervisory control theory are extended to the setting of $\omega $-languages, formal languages consisting of infinite strings. The extension permits the investigation of both liveness and safety issues in the control of discrete-event systems. A new controllability property appropriate to the infinitary setting ($\omega $-controllability) is defined; this language property captures in a natural way the limitations of available control actions. It is shown that every specification language contains a unique maximal $\omega $-controllable sublanguage, representing the least upper bound of the set of achievable closed-loop sublanguages. This supremal w-controllable sublanguage allows a simple formulation of necessary and sufficient conditions for the solvability of an infinitary supervisory control problem. The problems of effectively deciding solvability of the control problem and of effectively synthesizing appropriate supervisors are solved for the case where the plant is represented by a deterministic Buchi automaton and the specification of legal behavior by a deterministic Rabin automaton. |
| doi_str_mv | 10.1137/S0363012991217524 |
| format | Article |
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| identifier | ISSN: 0363-0129 |
| ispartof | SIAM journal on control and optimization, 1994-07, Vol.32 (4), p.1098-1113 |
| issn | 0363-0129 1095-7138 |
| language | eng |
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| source | SIAM journals (Society for Industrial and Applied Mathematics) |
| subjects | Applied sciences Computer science control theory systems Control theory Control theory. Systems Exact sciences and technology Language Supervision Supervisors System theory |
| title | Supervision of infinite behavior of discrete-event systems |
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