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New results on supervisor localization, with case studies

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Abstract

Recently we developed supervisor localization, a top-down approach to distributed control of discrete-event systems in the Ramadge-Wonham supervisory control framework. Its essence is the allocation of monolithic (global) control action among the local control strategies of individual agents. In this paper, we start by presenting several refinements of our localization theory. First, we drop the original assumption that the event sets of component agents are pairwise disjoint. Second, we show that consistent marking information can be enforced by just one agent, which can be selected arbitrarily. Third, the event sets of localized controllers are explicitly defined, in general as proper subsets of the entire event set. For these generalizations, we again prove that the collective local controlled behavior is identical to the global optimal and nonblocking controlled behavior. Moreover, we provide a language interpretation of localization by relating the key concept of control cover/congruence on the supervisor’s state set to a special right congruence on the supervisor’s language.W e go on to apply the extended supervisor localization to solve a multi-agent formation problem. We introduce a suitable formulation of formation invariance as well as shortest paths to formation. Local strategies are synthesized for a group of agents to arrive at a pre-specified formation in shortest paths; then issues of information exchange and control logic are examined. We further demonstrate the extended localization on a large-scale Cluster Tool example. By first synthesizing a set of decentralized supervisors and coordinators by an efficient heterarchical approach, our localization yields a distributed control architecture with comprehensible local control/coordination logic.

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Notes

  1. In this paper the notation [1,n] is used for the integer interval {1,...,n}.

  2. Computation in this and next sections is by TCT software (Wonham 2013a).

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Authors and Affiliations

  1. Urban Research Plaza, Osaka City University, Osaka, Japan

    Kai Cai

  2. Systems Control Group, Department of Electrical and Computer Engineering, University of Toronto, Toronto, Canada

    W. M. Wonham

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  1. Kai Cai
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  2. W. M. Wonham
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Correspondence to Kai Cai.

Additional information

This work was supported in part by Program to Disseminate Tenure Tracking System, MEXT, Japan (Kai Cai).

This work was supported in part by the Natural Sciences and Engineering Research Council, Canada, Grant no. 7399 (W. M. Wonham).

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Cai, K., Wonham, W.M. New results on supervisor localization, with case studies. Discrete Event Dyn Syst 25, 203–226 (2015). https://doi.org/10.1007/s10626-014-0194-6

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  • DOI: https://doi.org/10.1007/s10626-014-0194-6

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