Compositional Abstraction and Safety Synthesis Using Overlapping Symbolic Models

In this paper, we develop a compositional approach to abstraction and safety synthesis for a general class of discrete-time nonlinear systems. Our approach makes it possible to define a symbolic abstraction by composing a set of symbolic subsystems that are overlapping in the sense that they can sha...

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Published in:	IEEE transactions on automatic control Vol. 63; no. 6; pp. 1835 - 1841
Main Authors:	Meyer, Pierre-Jean, Girard, Antoine, Witrant, Emmanuel
Format:	Journal Article
Language:	English
Published:	IEEE 01.06.2018 Institute of Electrical and Electronics Engineers
Subjects:	Aerospace electronics Automatic Automatic control Computational modeling Computer Science Concrete control design Control systems Electronic mail Engineering Sciences formal verification Integrated circuits Mathematics nonlinear control systems Optimization and Control Safety scalability Systems and Control temperature control
ISSN:	0018-9286, 1558-2523, 1558-2523
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Abstract	In this paper, we develop a compositional approach to abstraction and safety synthesis for a general class of discrete-time nonlinear systems. Our approach makes it possible to define a symbolic abstraction by composing a set of symbolic subsystems that are overlapping in the sense that they can share some common state variables. We develop compositional safety synthesis techniques using such overlapping symbolic subsystems. Comparisons, in terms of conservativeness and of computational complexity, between abstractions and controllers obtained from different system decompositions are provided. Numerical experiments show that the proposed approach for symbolic control synthesis enables a significant complexity reduction with respect to the centralized approach, while reducing the conservatism with respect to compositional approaches using nonoverlapping subsystems.
AbstractList	In this paper, we develop a compositional approach to abstraction and safety synthesis for a general class of discrete-time nonlinear systems. Our approach makes it possible to define a symbolic abstraction by composing a set of symbolic subsystems that are overlapping in the sense that they can share some common state variables. We develop compositional safety synthesis techniques using such overlapping symbolic subsystems. Comparisons, in terms of conservativeness and of computational complexity, between abstractions and controllers obtained from different system decompositions are provided. Numerical experiments show that the proposed approach for symbolic control synthesis enables a significant complexity reduction with respect to the centralized approach, while reducing the conservatism with respect to compositional approaches using nonoverlapping subsystems. In this paper, we develop a compositional approach to abstraction and safety synthesis for a general class of discrete time nonlinear systems. Our approach makes it possible to define a symbolic abstraction by composing a set of symbolic subsystems that are overlapping in the sense that they can share some common state variables. We develop compositional safety synthesis techniques using such overlapping symbolic subsystems. Comparisons, in terms of conservativeness and of computational complexity, between abstractions and controllers obtained from different system decompositions are provided. Numerical experiments show that the proposed approach for symbolic control synthesis enables a significant complexity reduction with respect to the centralized approach, while reducing the conservatism with respect to compositional approaches using non-overlapping subsystems.
Author	Girard, Antoine Meyer, Pierre-Jean Witrant, Emmanuel
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References	ref13 ref15 ref14 ref31 ref30 ref11 baier (ref4) 2008 ref2 ref1 ref17 ref16 ref18 meyer (ref19) 2015 girard (ref12) 2005 ref24 ref23 ref26 ref25 cassandras (ref9) 2009 ref20 ref21 coogan (ref10) 2015 ref27 ref29 ref8 ref7 ref3 ref5 pola (ref22) 2016 ben sassi (ref6) 2012 tazaki (ref28) 2008
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SubjectTerms	Aerospace electronics Automatic Automatic control Computational modeling Computer Science Concrete control design Control systems Electronic mail Engineering Sciences formal verification Integrated circuits Mathematics nonlinear control systems Optimization and Control Safety scalability Systems and Control temperature control
Title	Compositional Abstraction and Safety Synthesis Using Overlapping Symbolic Models
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