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On the persistency of excitation

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2023 Belgium, Spain English Publisher:Elsevier BVJournal:Automatica, volume 147, page 110,657 (issn: 0005-1098,

Authors: Markovsky, Ivan; Prieto Araujo, Eduardo; Dörfler, Florian;

doi: 10.1016/j.automatica.2022.110657

handle: 2117/381187

On the persistency of excitation

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Abstract

The result of J.C. Willems et al. “A note on persistency of excitation”, System & Control Letters, 2005 gives identifiability conditions for system identification as well as data-driven representations for data-driven control. The existing proofs however are proofs by contradiction and do not give insight into the assumptions of controllability and persistency of excitation of the input. Moreover, the existing proofs do not clarify how conservative the assumptions are. We provide an alternative constructive proof for the single-input case. It is shown that persistency of excitation of order more than the time horizon is needed in nongeneric cases, corresponding to special initial conditions. The special initial conditions are explicitly characterized in terms of the solution of a Sylvester equation. Another contribution of the paper is a representation of a scalar persistently exciting input of a finite order as an output of an autonomous linear time-invariant system

Peer Reviewed

Countries

Belgium, Spain

Related Organizations

International Center for Numerical Methods in Engineering
Spain
Universitat Politècnica de Catalunya
Spain
Universitat Polite`cnica de Catalunya
Spain
ETH Zurich
Switzerland
Automatic Control Laboratory
Switzerland

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Keywords

Technology, Exact identification, 46 Information and computing sciences, 09 Engineering, 510, Automation & Control Systems, Engineering, SYSTEMS, STADIUS-25-83, Identifiability, Input design, Behavioral approach, 01 Mathematical Sciences, 40 Engineering, Science & Technology, Àrees temàtiques de la UPC::Enginyeria elèctrica, Persistency of excitation, Engineering, Electrical & Electronic, Persistency of excitation Input design, Industrial Engineering & Automation, Electrical engineering, Energia elèctrica, 08 Information and Computing Sciences, 49 Mathematical sciences

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