We present an observer for parameter estimation in nonlinear oscillating systems (periodic, quasiperiodic or chaotic). The observer requires measurements of generalized displacements. It estimates generalized velocities on a fast time scale and unknown parameters on a slow time scale, with time scale separation specified by a small parameter ε. Parameter estimates converge asymptotically like where is time, provided the data is such that a certain averaged coefficient matrix is positive definite. The method is robust: small model errors and noise cause small estimation errors. The effects of zero mean, high frequency noise can be reduced by faster sampling. Several numerical examples show the effectiveness of the method.
Asymptotic Parameter Estimation via Implicit Averaging on a Nonlinear Extended System
Contributed by the Dynamic Systems and Control Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the ASME Dynamic Systems and Control Division, December 1999; final revision, July 2002. Associate Editor: S. Fassois.
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Chatterjee, A., and Cusumano, J. P. (March 10, 2003). "Asymptotic Parameter Estimation via Implicit Averaging on a Nonlinear Extended System ." ASME. J. Dyn. Sys., Meas., Control. March 2003; 125(1): 11–18. https://doi.org/10.1115/1.1540638
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