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A Markov Chain Approach to Compute the ℓ2-gain of Nonlinear Systems
KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).ORCID iD: 0000-0002-6322-7857
KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).ORCID iD: 0000-0003-0355-2663
2018 (English)Conference paper, Published paper (Refereed)
Abstract [en]

In this work the problem of computing the maximum gain of non-linear systems, also known as its ℓ2-gain, from input-output data is studied. From an input design perspective, this problem reduces to find an optimal input sequence, of bounded norm, maximizing the norm gain of the output, where our target estimation corresponds to the ratio of these quantities. The novelty of this approach lies on the fact that the input signal is a realization of a stationary process with finite memory whose range is a finite set of values. Based on recent developents on input design for nonlinear systems, our approach leads to a linear program whose optimal cost gives an approximation of the ℓ2-gain of the system. An illustrative example shows how well the algorithm performs compared to other methods approximating this quantity.

Place, publisher, year, edition, pages
Elsevier B.V. , 2018. Vol. 51, no 15, p. 84-89
Keywords [en]
excitation design, identification for control, Input, non-linear system identification, ℓ2-gain, Linear programming, Linear systems, Markov processes, Input-output data, Linear programs, Markov chain approaches, Stationary process, Target estimations, Nonlinear systems
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-247492DOI: 10.1016/j.ifacol.2018.09.095ISI: 000446599200016Scopus ID: 2-s2.0-85054461369OAI: oai:DiVA.org:kth-247492DiVA, id: diva2:1305766
Conference
18th IFAC Symposium on System Identification
Note

QC 20190418

Available from: 2019-04-18 Created: 2019-04-18 Last updated: 2020-03-04Bibliographically approved

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Müller, Matias I.Rojas, Cristian R.

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CiteExportLink to record
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