NDLI: Symbolic Control of Stochastic Systems via Approximately Bisimilar Finite Abstractions

Content Provider	IEEE Xplore Digital Library
Author	Zamani, M. Mohajerin Esfahani, P. Majumdar, R. Abate, A. Lygeros, J.
Copyright Year	1963
Abstract	Symbolic approaches for control design construct finite-state abstract models that are related to the original systems, then use techniques from finite-state synthesis to compute controllers satisfying specifications given in a temporal logic, and finally translate the synthesized schemes back as controllers for the original systems. Such approaches have been successfully developed and implemented for the synthesis of controllers over non-probabilistic control systems. In this paper, we extend the technique to probabilistic control systems modelled by controlled stochastic differential equations. We show that for every stochastic control system satisfying a probabilistic variant of incremental input-to-state stability, and for every given precision ε > 0, a finite-state transition system can be constructed, which is ε-approximately bisimilar to the original stochastic control system. Moreover, we provide results relating stochastic control systems to their corresponding finite-state transition systems in terms of probabilistic bisimulation relations known in the literature. We demonstrate the effectiveness of the construction by synthesizing controllers for stochastic control systems over rich specifications expressed in linear temporal logic. Our technique enables automated, correct-by-construction, controller synthesis for stochastic control systems, which are common mathematical models employed in many safety critical systems subject to structured uncertainty.
Sponsorship	IEEE Control Systems Society
Starting Page	3135
Ending Page	3150
Page Count	16
File Size	587521
File Format	PDF
ISSN	00189286
Volume Number	59
Issue Number	12
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Control systems Stochastic processes Lyapunov methods Stability analysis Probabilistic logic Computational modeling Approximation methods stochastic systems Automated synthesis bisimulation incremental stability linear temporal logic
Content Type	Text
Resource Type	Article
Subject	Control and Systems Engineering Electrical and Electronic Engineering Computer Science Applications

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