Control of Non-Deterministic Systems With <i>μ</i>-Calculus Specifications Using Quotienting

Samik Basu; Ratnesh Kumar

doi:10.1109/JAS.2021.1003964

Volume 8 Issue 5

May 2021

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2021 > 8(5): 953-970

S. Basu, R. 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

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S. Basu, R. 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

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

doi: 10.1109/JAS.2021.1003964

Samik Basu^1
,,
Ratnesh Kumar^{2
,
,}

1.
Department of Computer Science, Iowa State University, Iowa 50011-3060 USA
2.
Department of Electrical and Computer Engineering, Iowa State University, Iowa 50011-3060 USA

Funds: The work was supported in part by the National Science Foundation (NSF-ECCS-1509420, NSF-CSSI-2004766)

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Author Bio:
Samik Basu is Professor in the Department of Computer Science at Iowa State University, USA. His research interests include formal methods, software verification, social network analysis, preference reasoning and security. He received the B.E. in computer science and engineering from Jadavpur University, India, in 1998, and the M.S. and Ph.D. degrees in computer science from Stony Brook University in 2001 and 2003, respectively

Ratnesh Kumar (F’07) is a Harpole Professor at the Department of Electrical and Computer Engineering at Iowa State University, where he directs the ESSeNCE (Embedded Software, Sensors, Networks, Cyberphysical, and Energy) Lab. Previously, he held faulty position at the University of Kentucky, and various visiting positions with the University of Maryland (College Park), the Applied Research Laboratory at the Pennsylvania State University (State College), the NASA Ames, the Idaho National Laboratory, the United Technologies Research Center, and the Air Force Research Laboratory. He received the B.Tech. degree in electrical engineering from IIT, India, in 1987, and the M.S. and Ph.D. degrees in electrical and computer engineering from The University of Texas at Austin in 1989 and 1991, respectively. He was a recipient of the Gold Medals for the Best EE Undergrad, the Best EE Project, and the Best All Rounder from IIT Kanpur, the Best Dissertation Award from UT Austin, the Best Paper Award from the IEEE Transactions on Automation Science and Engineering, and Keynote Speaker and paper awards recipient from multiple conferences. He is or has been an Editor of several journals (including of IEEE, SIAM, ACM, Springer, IET, MDPI), was a Distinguished Lecturer of the IEEE Control Systems Society, is a recipient of D. R. Boylan Eminent Faculty Award for Research from Iowa State University, a Fellow of IEEE, and also a Fellow of AAAS
Corresponding author: Ratnesh Kumar, e-mail: rkumar@iastate.edu
Received Date: 2020-09-23
Revised Date: 2020-12-10
Accepted Date: 2021-01-10

Available Online: 2021-02-02

Abstract

Abstract

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.
- Discrete event systems (DES),
- non-deterministic plant,
- μ-calculus,
- supervisory control

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References

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

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