# Asymptotic Parameter Estimation via Implicit Averaging on a Nonlinear Extended System

Chatterjee, Anindya and Cusumano, Joseph P (2002) Asymptotic Parameter Estimation via Implicit Averaging on a Nonlinear Extended System. In: Journal of Dynamic Systems, Measurement, and Control, 125 (1). pp. 11-18.

 PDF Asymptotic_Parameter_Estimation.pdf Restricted to Registered users only Download (157Kb) | Request a copy

## Abstract

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 $\epsilon$. Parameter estimates converge asymptotically like $e–^{-{\epsilon}t}$ where t 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.

Item Type: Journal Article Copyright of this article belongs to American Society of Mechanical Engineers . Division of Mechanical Sciences > Mechanical Engineering 01 Jun 2006 19 Sep 2010 04:28 http://eprints.iisc.ernet.in/id/eprint/7236