Data-Driven Identification of Dissipative Linear Models for Nonlinear Systems

We consider the problem of identifying a dissipative linear model of an unknown nonlinear system that is known to be dissipative, from time-domain input-output data. We first learn an approximate linear model of the nonlinear system using standard system identification techniques and then perturb th...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 67; no. 9; pp. 4978 - 4985
Main Authors Sivaranjani, S., Agarwal, Etika, Gupta, Vijay
Format Journal Article
LanguageEnglish
Published New York IEEE 01.09.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Circuit stability
Data models
Dissipation
Dissipativity
identification
Integrated circuit modeling
learning
Mathematical analysis
Matrices (mathematics)
Nonlinear systems
passivity
Perturbation
Perturbation methods
Stability criteria
System identification
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Summary:We consider the problem of identifying a dissipative linear model of an unknown nonlinear system that is known to be dissipative, from time-domain input-output data. We first learn an approximate linear model of the nonlinear system using standard system identification techniques and then perturb the system matrices of the linear model to enforce dissipativity, while closely approximating the dynamical behavior of the nonlinear system. Further, we provide an analytical relationship between the size of the perturbation and the radius in which the dissipativity of the linear model guarantees local dissipativity of the unknown nonlinear system. We demonstrate the application of this identification technique through two examples.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2022.3180810