Finding the weakest link(s): Coalition games for decentralized discrete-event control

In decentralized discrete-event system (DES) architectures, agents fuse their local decisions to arrive at the global decision. The contribution of each agent to the final decision is never assessed; however, it may be the case that only a subset of agents, i.e., a (static) coalition, perpetually contribute towards the correct final decisions. In casting the decentralized DES control (with and without communication) problem as a cooperative game, it is possible to quantify the average contribution that each agent makes towards synthesizing the overall correct control strategy. Specifically, we explore allocations that assess contributions of non-communicating and communicating controllers for this class of problems. This allows a quantification of the contribution that each agent makes to the coalition with respect to decisions made solely based on its partial observations and decisions made based on messages sent to another agent(s) to facilitate a correct control decision.

[1]  Rémi Morin,et al.  Decompositions of Asynchronous Systems , 1998, CONCUR.

[2]  Stéphane Lafortune,et al.  Decentralized supervisory control with communicating controllers , 2000, IEEE Trans. Autom. Control..

[3]  L. S. Shapley,et al.  17. A Value for n-Person Games , 1953 .

[4]  Stéphane Lafortune,et al.  A General Architecture for Decentralized Supervisory Control of Discrete-Event Systems , 2002, Discret. Event Dyn. Syst..

[5]  W H Sadid,et al.  Nash equilibrium for communication protocols in decentralized discrete-event systems , 2010, Proceedings of the 2010 American Control Conference.

[6]  Jan H. van Schuppen,et al.  Maximal Solutions in Decentralized Supervisory Control , 2000, SIAM J. Control. Optim..

[7]  Eduardo F. Camacho,et al.  A coalitional control scheme with applications to cooperative game theory , 2014 .

[8]  M. Dufwenberg.  Game theory. , 2011, Wiley interdisciplinary reviews. Cognitive science.

[9]  Oskar Skibski,et al.  Algorithms for the shapley and myerson values in graph-restricted games , 2014, AAMAS.

[10]  Md. Waselul Haque Sadid,et al.  Multiobjective optimization in control with communication for decentralized discrete-event systems , 2011, IEEE Conference on Decision and Control and European Control Conference.

[11]  Matthew O. Jackson,et al.  Allocation Rules for Network Games , 2003, Games Econ. Behav..

[12]  Stéphane Lafortune,et al.  Decentralized supervisory control with conditional decisions: supervisor existence , 2004, IEEE Transactions on Automatic Control.

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

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

[15]  Roger B. Myerson,et al.  Graphs and Cooperation in Games , 1977, Math. Oper. Res..

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

[17]  Volker Diekert,et al.  The Book of Traces , 1995 .

[18]  André Arnold,et al.  Finite transition systems , 1994 .

[19]  Jason R. Marden,et al.  Game Theory and Distributed Control , 2015 .

[20]  David P. L. Thorsley,et al.  Applications of stochastic techniques to partially observed discrete event systems. , 2006 .

[21]  Michel Grabisch,et al.  An allocation rule for dynamic random network formation processes , 2015 .

[22]  S. Ricker.  Asymptotic minimal communication for decentralized discrete-event control , 2008, 2008 9th International Workshop on Discrete Event Systems.