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A Combined Estimator for Nonlinear System Identification via LPV Approximations
  • Sadegh Ebrahimkhani,
  • John Lataire
Sadegh Ebrahimkhani
Vrije Universiteit Brussel

Corresponding Author:sadegh.ebrahimkhani@vub.be

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John Lataire
Vrije Universiteit Brussel
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Abstract

This paper addresses the identification of Nonlinear (NL) systems using a linearization approach, introducing a combined estimator to tackle this challenge. We assume that the unknown NL system operates around a stable, slowly varying operating point. The system trajectory is then perturbed slightly via small, typically fast, input perturbations. We demonstrate that the NL system’s response to these small perturbations can be approximated by a Linear Parameter-Varying (LPV) system model. Furthermore, we show that this LPV model represents the linearized version of the unknown NL system around the operating point. A new parametrization for the LPV model coefficients is introduced, establishing a structural relationship between the LPV coefficients. This structural relationship reduces the number of parameters to be estimated and ensures that the LPV model always corresponds to the linearized form of the NL system. Additionally, we demonstrate that this LPV model structure allows for the unique reconstruction of the NL system model through symbolic integration, resulting in a closed-form nonlinear Ordinary Differential Equation (ODE). This integration introduces a second structural relationship, linking the LPV model to the NL model. By leveraging these two structural relationships, we reformulate the problem of NL system identification via linearization as a combined estimation problem, leading to a unified LPV-NL estimation framework. This approach utilizes all available data, including perturbation data (linear response) and the varying operating point (NL response). We propose a combined estimator that jointly estimates the NL-LPV model, capturing the intrinsic structure of NL system identification through linearization. Finally, we present a numerical example to illustrate the performance of the proposed method.
10 Oct 2024Submitted to International Journal of Robust and Nonlinear Control
11 Oct 2024Submission Checks Completed
11 Oct 2024Assigned to Editor
11 Oct 2024Review(s) Completed, Editorial Evaluation Pending
13 Oct 2024Reviewer(s) Assigned