Supremal and maximal sublanguages arising in supervisor synthesis problems with partial observations

The paper studies in a unified manner both the class of closed, (Σu,N)-invariant, and (M, N)-recognizable sublanguages and the class of closed, (Σu,N)-invariant, and (M, Σc,N)-controllable sublanguages of a given languageL that arise in supervisor synthesis problems of discrete event dynamical systems with partial observations. The supremal element of the former class is often too restrictive, and it is natural to study maximal elements of the latter class. A procedure which computes such a maximal element as a limit of a decreasing sequence of sublanguages ofL is presented. Each term of the sequence is shown to be regular if a slightly modified procedure is used.

[1]  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..

[2]  Roland Fraïssé.  Theory of relations , 1986 .

[3]  P. Ramadge.  Some tractable supervisory control problems for discrete-event systems modeled by Buchi automata , 1989 .

[4]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

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

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

[7]  守屋 悦朗,et al.  J.E.Hopcroft, J.D. Ullman 著, "Introduction to Automata Theory, Languages, and Computation", Addison-Wesley, A5変形版, X+418, \6,670, 1979 , 1980 .

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

[9]  Thomas Sudkamp,et al.  Languages and Machines , 1988 .

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

[11]  P. Ramadge,et al.  Modular feedback logic for discrete event systems , 1987 .

[12]  Samuel Eilenberg,et al.  Automata, languages, and machines. A , 1974, Pure and applied mathematics.

[13]  Stéphane Lafortune.  Modeling and analysis of transaction execution in database systems , 1988 .

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

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

[16]  P. Ramadge,et al.  Modular Supervisory Control of Discrete Event Systems , 1988 .