Computing supremal minimum-weight controllable and normal sublanguages

In practical applications we are frequently required to find a supervisor that can achieve certain optimal performance. Some performance such as maximum throughput or minimum execution time/cost can be specified in terms of weights. In this paper we first define a minimum-weight supervisory control problem on weighted discrete-event systems. Then we show that, the supremal minimum-weight controllable and normal sublanguages exist, and can be computed by a terminable algorithm.

[1]  Joseph Sifakis,et al.  Controller Synthesis for Timed Automata 1 , 1998 .

[2]  Krishnendu Chatterjee,et al.  Mean-payoff parity games , 2005, 20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05).

[3]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

[4]  Vijay K. Garg,et al.  Optimal Supervisory Control of Discrete Event DynamicalSystems , 1995 .

[5]  Vijay K. Garg,et al.  Control of stochastic discrete event systems modeled by probabilistic languages , 2001, IEEE Trans. Autom. Control..

[6]  George J. Pappas,et al.  Optimal Paths in Weighted Timed Automata , 2001, HSCC.

[7]  D. Bertsekas,et al.  Stochastic Shortest Path Games , 1999 .

[8]  Claude Berge,et al.  The Theory Of Graphs , 1962 .

[9]  Michael Heymann,et al.  On optimal attraction in discrete-event processes , 1993, Inf. Sci..

[10]  S. Lafortune,et al.  Optimal control of discrete event systems under partial observation , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[11]  A. Ehrenfeucht,et al.  Positional strategies for mean payoff games , 1979 .

[12]  Joseph Sifakis,et al.  On the Synthesis of Discrete Controllers for Timed Systems (An Extended Abstract) , 1995, STACS.

[13]  Yonghua Li,et al.  Supervisory control of probabilistic discrete-event systems with recovery , 1999, IEEE Trans. Autom. Control..

[14]  Fernando Pereira,et al.  Weighted finite-state transducers in speech recognition , 2002, Comput. Speech Lang..

[15]  Alan R. Washburn,et al.  Deterministic graphical games , 1990 .

[16]  Stavros Tripakis,et al.  On-the-Fly Controller Synthesis for Discrete and Dense-Time Systems , 1999, World Congress on Formal Methods.

[17]  Supratik Mukhopadhyay,et al.  Optimal-Reachability and Control for Acyclic Weighted Timed Automata , 2002, IFIP TCS.

[18]  George J. Pappas,et al.  Optimal Paths in Weighted Timed Automata , 2001, HSCC.

[19]  Mehryar Mohri.  Edit-Distance Of Weighted Automata: General Definitions And Algorithms , 2003, Int. J. Found. Comput. Sci..

[20]  H. Kushner,et al.  Finite state stochastic games: Existence theorems and computational procedures , 1969 .

[21]  R. Sengupta,et al.  An Optimal Control Theory for Discrete Event Systems , 1998 .

[22]  Ariel Rubinstein,et al.  A Course in Game Theory , 1995 .

[23]  Shengwei Ding,et al.  Throughput Analysis of Linear Cluster Tools , 2007, 2007 IEEE International Conference on Automation Science and Engineering.

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

[25]  Eugene Asarin,et al.  As Soon as Possible: Time Optimal Control for Timed Automata , 1999, HSCC.

[26]  S. Alpern.  Cycles in extensive form perfect information games , 1991 .

[27]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[28]  W. Wonham,et al.  Probability measure on regular languages and its application in fault diagnosis for discrete event systems , 2004, 2004 5th Asian Control Conference (IEEE Cat. No.04EX904).

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

[30]  K. Passino,et al.  On the optimal control of discrete event systems , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[31]  L. Shapley,et al.  Stochastic Games* , 1953, Proceedings of the National Academy of Sciences.