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Nonlinear Continuous-time System Identification by Linearization around a Time-varying setpoint
  • Sadegh Ebrahimkhani,
  • Mehrad Ghasem Sharabiany,
  • John Lataire
Sadegh Ebrahimkhani
Vrije Universiteit Brussel - Brussels Humanities Sciences & Engineering Campus
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Mehrad Ghasem Sharabiany
Vrije Universiteit Brussel - Brussels Humanities Sciences & Engineering Campus
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John Lataire
Vrije Universiteit Brussel - Brussels Humanities Sciences & Engineering Campus

Corresponding Author:[email protected]

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Abstract

This paper handles the identification of nonlinear systems through linear time-varying (LTV) approximation. The mathematical form of the nonlinear system is unknown and regenerated through an experiment followed by LTV and linear parameter-varying (LPV) estimation and integration. By employing a well-designed experiment the linearized model of the nonlinear system around a time-varying trajectory is obtained. The result is an LTV approximation of the nonlinear system around that trajectory. Having estimated the LTV model, an LPV model is identified. It is shown that the parameter-varying (PV) coefficients of this LPV model are partial derivatives of the nonlinear system evaluated at the trajectory. In this paper, we will show that there exists a relation between the LPV coefficients. This structural relation in the LPV model ensures the integrability of PV coefficients for nonlinear reconstruction. Indeed, the vector of the LPV coefficients is the gradient of the nonlinear system evaluated at the trajectory. Then, the nonlinear system is reconstructed through symbolic integration of the coefficients. The proposed method is a data-driven scheme that can reconstruct an estimate of the nonlinear system and its mathematical form using input-output measurements. Finally, the use of the proposed method is illustrated via a simulation example.
20 Jun 2023Submitted to International Journal of Robust and Nonlinear Control
20 Jun 2023Submission Checks Completed
20 Jun 2023Assigned to Editor
20 Jun 2023Review(s) Completed, Editorial Evaluation Pending
22 Jun 2023Reviewer(s) Assigned
27 Aug 2023Editorial Decision: Revise Minor
17 Mar 20242nd Revision Received
18 Mar 2024Submission Checks Completed
18 Mar 2024Assigned to Editor
18 Mar 2024Review(s) Completed, Editorial Evaluation Pending
18 Mar 2024Reviewer(s) Assigned
02 Apr 2024Editorial Decision: Revise Minor
26 Jun 20243rd Revision Received
26 Jun 2024Submission Checks Completed
26 Jun 2024Assigned to Editor
26 Jun 2024Review(s) Completed, Editorial Evaluation Pending