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Instrumental variable framework for nonlinear continuous-time system identification
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DOI：10.1016/j.jfranklin.2026.108619.png)
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Abstract
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This paper presents NLIVSVF, an iterative instrumental variable estimator for nonlinear continuous-time output-error models based on sampled input-output data. The method uses continuous-discrete extended Kalman filter-based derivative estimates to compute the nonlinear terms required for forming a linear regression used in parameter estimation. The resulting regression is solved using an instrumental variable procedure. Sparse model structures are identified through regression over libraries of candidate nonlinear terms, enabling parsimonious model discovery. By formulating the identification problem directly in continuous time, the approach avoids intermediate discretization. The method is evaluated on a simulated nonlinear system with both known and unknown nonlinearities, demonstrating reliable performance under stiff dynamics and noisy measurements.
Keywords:
Control systems
Continuous-time models
Instrumental variable
Nonlinear systems
Parameter estimation
Sparse regression
System identification
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