On the design of persistently exciting inputs for data-driven control of linear and nonlinear systems

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Original languageEnglish
Pages (from-to)2629 - 2634
JournalIEEE Control Systems Letters
Volume7
Publication statusPublished - 16 Jun 2023

Abstract

In the context of data-driven control, persistence of excitation (PE) of an input sequence is defined in terms of a rank condition on the Hankel matrix of the input data. For nonlinear systems, recent results employed rank conditions involving collected input and state/output data, for which no guidelines are available on how to satisfy them a priori. In this letter, we first show that a set of discrete impulses is guaranteed to be persistently exciting for any controllable LTI system. Based on this result, for certain classes of nonlinear systems, we guarantee persistence of excitation of sequences of basis functions a priori, by design of the physical input only.

Keywords

    Data-driven control, identification for control, persistence of excitation

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On the design of persistently exciting inputs for data-driven control of linear and nonlinear systems. / Alsalti, Mohammad Salahaldeen Ahmad; Lopez Mejia, Victor Gabriel; Müller, Matthias A.
In: IEEE Control Systems Letters, Vol. 7, 16.06.2023, p. 2629 - 2634.

Research output: Contribution to journalArticleResearchpeer review

Alsalti MSA, Lopez Mejia VG, Müller MA. On the design of persistently exciting inputs for data-driven control of linear and nonlinear systems. IEEE Control Systems Letters. 2023 Jun 16;7:2629 - 2634. doi: 10.48550/arXiv.2303.08707, 10.1109/LCSYS.2023.3287133
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T1 - On the design of persistently exciting inputs for data-driven control of linear and nonlinear systems

AU - Alsalti, Mohammad Salahaldeen Ahmad

AU - Lopez Mejia, Victor Gabriel

AU - Müller, Matthias A.

N1 - Funding Information: This work was supported by the European Research Council (ERC) through the European Union's Horizon 2020 Research and Innovation Programme under Grant 948679.

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