Discrete Abstractions of Nonlinear Systems Based on Error Propagation Analysis

This paper proposes a computational method for the feasibility check and design of discrete abstract models of nonlinear dynamical systems. First, it is shown that a given discrete-time dynamical system can be transformed into a finite automaton by embedding a quantizer into its state equation. Unde...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 57; no. 3; pp. 550 - 564
Main Authors Tazaki, Y., Imura, J.
Format Journal Article
LanguageEnglish
Published New York, NY IEEE 01.03.2012
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
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Summary:This paper proposes a computational method for the feasibility check and design of discrete abstract models of nonlinear dynamical systems. First, it is shown that a given discrete-time dynamical system can be transformed into a finite automaton by embedding a quantizer into its state equation. Under this setting, a sufficient condition for approximate bisimulation in infinite steps of time between the concrete model and its discrete abstract model is derived. The condition takes the form of a set of linear inequalities and thus can be checked efficiently by a linear programming solver. Finally, the iterative refinement algorithm, which generates a discrete abstract model under a given error specification, is proposed. The algorithm is guaranteed to terminate in finite iterations.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2011.2161789