Direct data-driven state-feedback control of general nonlinear systems

Through the use of the Fundamental Lemma for linear systems, a direct data-driven state-feedback control synthesis method is presented for a rather general class of nonlinear (NL) systems. The core idea is to develop a data-driven representation of the so-called velocity-form, i.e., the time-differe...

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Bibliographic Details
Published in:arXiv.org 2023-09
Main Authors: Verhoek, Chris, Koelewijn, Patrick J W, Haesaert, Sofie, Tóth, Roland
Format: Article
Language:English
Subjects:
Basis functions
Closed loops
Control systems
Dissipation
Feedback control
Linear systems
Nonlinear control
Nonlinear systems
Representations
State feedback
Synthesis
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Summary:Through the use of the Fundamental Lemma for linear systems, a direct data-driven state-feedback control synthesis method is presented for a rather general class of nonlinear (NL) systems. The core idea is to develop a data-driven representation of the so-called velocity-form, i.e., the time-difference dynamics, of the NL system, which is shown to admit a direct linear parameter-varying (LPV) representation. By applying the LPV extension of the Fundamental Lemma in this velocity domain, a state-feedback controller is directly synthesized to provide asymptotic stability and dissipativity of the velocity-form. By using realization theory, the synthesized controller is realized as a NL state-feedback law for the original unknown NL system with guarantees of universal shifted stability and dissipativity, i.e., stability and dissipativity w.r.t. any (forced) equilibrium point, of the closed-loop behavior. This is achieved by the use of a single sequence of data from the system and a predefined basis function set to span the scheduling map. The applicability of the results is demonstrated on a simulation example of an unbalanced disc.
ISSN:2331-8422
DOI:10.48550/arxiv.2303.10648