Problems and Examples of Decentralized Observation and Control for Discrete Event Systems

We study decentralized observation and control problems for discrete event systems. For problems with a single observer or controller, it is well known that if a solution exists, then a finite-state solution also exists. We show that in the decentralized case there might not exist finite-state observers and controllers, even though infinite-state ones exist and the plant is finite-state. We also give necessary and sufficient conditions for finite-state observers to exist. We then formulate the problem of synthesizing a reliable transmission protocol on top of unreliable channels as a decentralized control problem, and present the well known alternating bit protocol (ABP) as a solution. We finally study the existence of solutions for variations of the reliable transmission problem, where one or both channels can carry only one symbol and are of finite or infinite capacity. We show that a solution exists if one of the forward or backward channels is two-symbol and the other one-symbol, whereas no solution exists if both are one-symbol.

[1]  M. Rabin.  Automata on Infinite Objects and Church's Problem , 1972 .

[2]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[3]  Jean Berstel,et al.  Transductions and context-free languages , 1979, Teubner Studienbücher : Informatik.

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

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

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

[7]  Walter Murray Wonham,et al.  Decentralized supervisory control of discrete-event systems , 1987, Inf. Sci..

[8]  W. M. Wonham,et al.  The control of discrete event systems , 1989 .

[9]  David L. Dill,et al.  Synthesizing Processes and Schedulers from Temporal Specifications , 1990, CAV.

[10]  Wolfgang Thomas,et al.  Automata on Infinite Objects , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[11]  Walter Murray Wonham,et al.  Supervisory control of communicating processes , 1990, PSTV.

[12]  Amir Pnueli,et al.  Distributed reactive systems are hard to synthesize , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[13]  W. Wonham,et al.  The infimal prefix-closed and observable superlanguage of given language , 1991 .

[14]  W. Murray Wonham,et al.  Think Globally, Act Locally: Decentralized Supervisory Control , 1991, 1991 American Control Conference.

[15]  W. M. Wonham,et al.  Protocol verification using discrete-event systems , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[16]  Max Donath,et al.  American Control Conference , 1993 .

[17]  S. D. Chatterji.  Proceedings of the International Congress of Mathematicians , 1995 .

[18]  J. Willems,et al.  The computational complexity of decentralized discrete-event control problems , 1995, IEEE Trans. Autom. Control..

[19]  Raja Sengupta,et al.  Diagnosability of discrete-event systems , 1995, IEEE Trans. Autom. Control..

[20]  K. C. Wong,et al.  Decentralized supervisory control of discrete-event systems with communication , 1996 .

[21]  M. Shayman,et al.  Centralized and Decentralized Supervisory Control of Nondeterministic Systems Under Partial Observation , 1997 .

[22]  Moshe Kam,et al.  Decision fusion and supervisor synthesis in decentralized discrete-event systems , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[23]  Stéphane Lafortune,et al.  On the synthesis of communicating controllers with decentralized information structures for discrete-event systems , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

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

[25]  Feng Lin,et al.  Minimal communication in a distributed discrete-event control system , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[26]  Orna Kupfermant,et al.  Synthesis with Incomplete Informatio , 2000 .

[27]  J. G. Thistle,et al.  Effective control synthesis for DES under partial observations , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[28]  Stéphane Lafortune,et al.  New results on decentralized supervisory control of discrete-event systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).