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Volume 8 Issue 5
May  2021

IEEE/CAA Journal of Automatica Sinica

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Samik Basu and Ratnesh Kumar, "Control of Non-Deterministic Systems With μ-Calculus Specifications Using Quotienting," IEEE/CAA J. Autom. Sinica, vol. 8, no. 5, pp. 953-970, May 2021. doi: 10.1109/JAS.2021.1003964
Citation: Samik Basu and Ratnesh Kumar, "Control of Non-Deterministic Systems With μ-Calculus Specifications Using Quotienting," IEEE/CAA J. Autom. Sinica, vol. 8, no. 5, pp. 953-970, May 2021. doi: 10.1109/JAS.2021.1003964

Control of Non-Deterministic Systems With μ-Calculus Specifications Using Quotienting

doi: 10.1109/JAS.2021.1003964
Funds:  The work was supported in part by the National Science Foundation (NSF-ECCS-1509420, NSF-CSSI-2004766)
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  • The supervisory control problem for discrete event system (DES) under control involves identifying the supervisor, if one exists, which, when synchronously composed with the DES, results in a system that conforms to the control specification. In this context, we consider a non-deterministic DES under complete observation and control specification expressed in action-based propositional μ-calculus. The key to our solution is the process of quotienting the control specification against the plan resulting in a new μ-calculus formula such that a model for the formula is the supervisor. Thus the task of control synthesis is reduced a problem of μ-calculus satisfiability. In contrast to the existing μ-calculus quotienting-based techniques that are developed in deterministic setting, our quotienting rules can handle nondeterminism in the plant models. Another distinguishing feature of our technique is that while existing techniques use a separate μ-calculus formula to describe the controllability constraint (that uncontrollable events of plants are never disabled by a supervisor), we absorb this constraint as part of quotienting which allows us to directly capture more general state-dependent controllability constraints. Finally, we develop a tableau-based technique for verifying satisfiability of quotiented formula and model generation. The runtime for the technique is exponential in terms of the size of the plan and the control specification. A better complexity result that is polynomial to plant size and exponential to specification size is obtained when the controllability property is state-independent. A prototype implementation in a tabled logic programming language as well as some experimental results are presented.

     

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