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Epistemic interpretations of decentralized discrete-event system problems

Abstract

This paper presents epistemic characterizations to co-observability conditions in decentralized supervisory control of discrete-event systems. The logical characterizations provide more intuitive interpretations of the various co-observability conditions, and make immediately apparent the relations between the conditions. Closures under set union of some of the conditions are also discussed.

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Notes

  1. Perhaps under the influence of Prosser et al. (1997), the work of Takai and Ushio (2001), which precedes Takai et al. (2005), reverses the meaning of 0 and 1. Hence their OR (resp., AND) rule corresponds to our conjunctive (resp., disjunctive) rule. We follow the more common convention here.

  2. The term “states” should cause no confusion in this context, since the worlds in the frames we construct in this work happen to be states of some FSA.

  3. Readers familiar with modal logics should note that by stating “have S” we do not mean that S is valid, i.e., S evaluates to true at every interpretation and every world, since that concept has not been defined here.

  4. For detailed discussion on the control decisions weak off and weak on, see the works by Yoo and Lafortune (2004) and Ricker and Rudie (2007) and Ean and Rudie (2021a) and Ean and Rudie (2021b). Note that Yoo and Lafortune (2004) and Ricker and Rudie (2007) use different names for the control decisions.

  5. The notion of higher levels of inferences is discussed by Kumar and Takai (2005). A visualization and some supplements are presented by Ean and Rudie (2021b), where the epistemic interpretation is also informally discussed.

  6. This result gives us an inspiration: given two languages L(E1) and L(E2) synthesisable in the architecture A, we should not confine ourselves in synthesizing the union language L(E) in the architecture A, but instead be willing to look for an alternative architecture B in which we can synthesize L(E). Then let all architectures ordered by their strength, we’d then like to ask: does there exist a supremal architecture?

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Acknowledgements

The research described in this paper was undertaken at Queen’s University, which is situated on traditional Anishinaabe and Haudenosaunee territory. The research was inspired by and supported through an NSERC CRD-DND project with General Dynamics Land Systems-Canada and Defence Research and Development Canada.

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Correspondence to Richard Ean.

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This work was financially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) through a Collaborative Research and Development Grant together with General Dynamics Land Systems (R.E.) and an NSERC Discovery Grant (K.R.).

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Ean, R., Rudie, K. Epistemic interpretations of decentralized discrete-event system problems. Discrete Event Dyn Syst 32, 359–398 (2022). https://doi.org/10.1007/s10626-022-00363-7

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Keywords

  • Discrete-event systems
  • Supervisory control
  • Epistemic logic