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Electrical Engineering and Systems Science > Systems and Control

arXiv:2505.07234 (eess)
[Submitted on 12 May 2025 (v1), last revised 11 Nov 2025 (this version, v2)]

Title:A Novel Online Pseudospectral Method for Approximation of Nonlinear Systems Dynamics

Authors:Arian Yousefian, Avimanyu Sahoo, Vignesh Narayanan
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Abstract:This note presents an online pseudospectral method for system identification using Chebyshev polynomial basis under aperiodic sampling. The system dynamics are approximated piecewise by introducing a sliding time window. The number of sampling instants (Chebyshev nodes) within each sliding window is selected dynamically based on a proposed node-selection criterion that guarantees desired approximation accuracy. The system states are measured at these aperiodic instants and used to estimate the coefficients of the basis polynomials using least squares. An adaptive state estimator is also proposed to reconstruct the continuous states using the approximated dynamics. The boundedness of the parameter and state estimation errors is proven analytically and validated numerically.
Comments: 8 pages, 5 figures, Substantially extends our earlier paper accepted for ACC 2025 (Denver, 8 Jul 2025). Submitted to IEEE Transactions on Automatic Control; under review
Subjects: Systems and Control (eess.SY)
Cite as: arXiv:2505.07234 [eess.SY]
  (or arXiv:2505.07234v2 [eess.SY] for this version)
  https://doi.org/10.48550/arXiv.2505.07234

Submission history

From: Arian Yousefian [view email]
[v1] Mon, 12 May 2025 05:19:53 UTC (8,113 KB)
[v2] Tue, 11 Nov 2025 02:28:17 UTC (335 KB)
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