Supervisory Control of Partially Observed Quantitative Discrete Event Systems for Fixed-Initial-Credit Energy Problem

This paper studies the supervisory control of partially observed quantitative discrete event systems (DESs) under the fixed-initialcredit energy objective. A quantitative DES is modeled by a weighted automaton whose event set is partitioned into a controllable event set and an uncontrollable event set. Partial observation is modeled by a mapping from each event and state of the DES to the corresponding masked event and masked state that are observed by a supervisor. The supervisor controls the DES by disabling or enabling any controllable event for the current state of the DES, based on the observed sequences of masked states and masked events. We model the control process as a two-player game played between the supervisor and the DES. The DES aims to execute the events so that its energy level drops below zero, while the supervisor aims to maintain the energy level above zero. We show that the proposed problem is reducible to finding a winning strategy in a turn-based reachability game. key words: supervisory control, discrete event system, partial observation, optimal control, energy game

[1]  L. Brim,et al.  Faster algorithms for mean-payoff games , 2011, Formal Methods Syst. Des..

[2]  Thomas A. Henzinger,et al.  Concurrent reachability games , 2007, Theor. Comput. Sci..

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

[4]  Krishnendu Chatterjee,et al.  Minimum Attention Controller Synthesis for Omega-Regular Objectives , 2011, FORMATS.

[5]  H. W. Kuhn,et al.  11. Extensive Games and the Problem of Information , 1953 .

[6]  Kim G. Larsen,et al.  Energy Games in Multiweighted Automata , 2011, ICTAC.

[7]  W. M. Wonham,et al.  Supervision of Infinite Behavior of Discrete-Event Systems , 1994 .

[8]  Philippe Schnoebelen,et al.  Ackermannian and Primitive-Recursive Bounds with Dickson's Lemma , 2010, 2011 IEEE 26th Annual Symposium on Logic in Computer Science.

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

[10]  Guillermo A. Pérez,et al.  The fixed initial credit problem for partial-observation energy games is Ack-complete , 2015, Inf. Process. Lett..

[11]  Krishnendu Chatterjee,et al.  Controller Synthesis with Budget Constraints , 2008, HSCC.

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

[13]  Toshimitsu Ushio,et al.  Quantitative Supervisory Control Game for Discrete Event Systems , 2016, IEEE Transactions on Automatic Control.

[14]  Szymon Torunczyk,et al.  Energy and Mean-Payoff Games with Imperfect Information , 2010, CSL.

[15]  Ralf Fröberg,et al.  An introduction to Gröbner bases , 1997, Pure and applied mathematics.

[16]  T. Ushio,et al.  A new class of supervisors for partially observed discrete event systems , 1995, Proceedings of 1995 American Control Conference - ACC'95.