A New Class of Supervisors for Timed Discrete Event Systems Under Partial Observation

Brandin and Wonham have developed a supervisory control framework for timed discrete event systems (TDESs) in order to deal with not only logical specifications but also temporal specifications. Lin and Wonham have extended this framework to the partial observation case, and presented necessary and sufficient conditions for the existence of a nonblocking supervisor under partial observation. In this paper, we define a new class of supervisors for TDESs under partial observation. We then present necessary and sufficient conditions for the existence of a nonblocking supervisor defined in this paper. These existence conditions of our supervisor are weaker than those of Lin and Wonham's supervisor. Note, however, that the price that must be paid to weaken the existence conditions is the higher computational cost. Moreover, given a closed regular language, we study computation of a sublanguage that satisfies the existence conditions of our supervisor. We present an algorithm for computing such a sublanguage larger than the supremal closed, controllable, and normal sublanguage.

[1]  W. M. Wonham,et al.  Modular supervisory control of timed discrete-event systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[2]  Walter Murray Wonham,et al.  Reduced supervisors for timed discrete-event systems , 2003, IEEE Trans. Autom. Control..

[3]  P. Ramadge,et al.  On the supermal controllable sublanguage of a given language , 1987 .

[4]  Walter Murray Wonham,et al.  On observability of discrete-event systems , 1988, Inf. Sci..

[5]  Toshimitsu Ushio,et al.  Effective computation of an Lm(G)-closed, controllable, and observable sublanguage arising in supervisory control , 2003, Syst. Control. Lett..

[6]  John N. Tsitsiklis,et al.  On the control of discrete-event dynamical systems , 1987, 26th IEEE Conference on Decision and Control.

[7]  Shigemasa Takai,et al.  Control-invariance of hybrid systems with forcible events , 2005, Autom..

[8]  Shigemasa Takai.  Robust supervisory control of a class of timed discrete event systems under partial observation , 2000 .

[9]  Shigemasa Takai,et al.  Supervisory Control of a Class of Concurrent Discrete Event Systems Under Partial Observation , 2003, SICE 2003 Annual Conference (IEEE Cat. No.03TH8734).

[10]  W. Wonham,et al.  Supervisory control of timed discrete-event systems under partial observation , 1995, IEEE Trans. Autom. Control..

[11]  Feng Lin,et al.  On-line control of partially observed discrete event systems , 1994, Discret. Event Dyn. Syst..

[12]  W. M. Wonham,et al.  Reduced supervisors for timed discrete-event systems , 2003, IEEE Trans. Autom. Control..

[13]  Sadatoshi Kumagai,et al.  Stabilization of Timed Discrete Event Systems with Forcible Events (Special Section of Selected Papers from the 9th Karuizawa Workshop on Circuits and Systems) , 1997 .

[14]  Walter Murray Wonham,et al.  Hierarchical control of timed discrete-event systems , 1996, Discret. Event Dyn. Syst..

[15]  Steven I. Marcus,et al.  On supremal languages of classes of sublanguages that arise in supervisor synthesis problems with partial observation , 1989, Math. Control. Signals Syst..

[16]  Tan-Jan Ho.  A new approach to synthesis problems in timed discrete-event systems , 2000 .

[17]  W. Wonham,et al.  Supervisory control of timed discrete-event systems , 1994, IEEE Trans. Autom. Control..

[18]  S. Takai,et al.  State feedback control of hybrid automata with forcible events , 2002, Sixth International Workshop on Discrete Event Systems, 2002. Proceedings..

[19]  P. Ramadge,et al.  On the supremal controllable sublanguage of a given language , 1984, The 23rd IEEE Conference on Decision and Control.

[20]  P. Ramadge,et al.  Supervisory control of a class of discrete event processes , 1987 .

[21]  C. Desclaux,et al.  Supervisory control of discrete-event processes with partial observations , 1988 .

[22]  Christos G. Cassandras,et al.  Introduction to Discrete Event Systems , 1999, The Kluwer International Series on Discrete Event Dynamic Systems.