Direct data-driven state-feedback control of general nonlinear systems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866913204340260864 |
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| author | Verhoek, Chris Koelewijn, Patrick J. W. Haesaert, Sofie Tóth, Roland |
| author_facet | Verhoek, Chris Koelewijn, Patrick J. W. Haesaert, Sofie Tóth, Roland |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_10648 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Direct data-driven state-feedback control of general nonlinear systems Verhoek, Chris Koelewijn, Patrick J. W. Haesaert, Sofie Tóth, Roland Systems and Control 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. |
| title | Direct data-driven state-feedback control of general nonlinear systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2303.10648 |