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Dynamic Algorithm for Parameter Estimation and Its Applications

Anil Maybhate·R. E. Amritkar
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Abstract

We consider a dynamic method, based on synchronization and adaptive control, to estimate unknown parameters of a nonlinear dynamical system from a given scalar chaotic time series. We present an important extension of the method when time series of a scalar function of the variables of the underlying dynamical system is given. We find that it is possible to obtain synchronization as well as parameter estimation using such a time series. We then consider a general quadratic flow in three dimensions and discuss applicability of our method of parameter estimation in this case. In practical situations one expects only a finite time series of a system variable to be known. We show that the finite time series can be repeatedly used to estimate unknown parameters with an accuracy which improves and then saturates to a constant value with repeated use of the time series. Finally we propose that the method can be used to confirm the correctness of a trial function modeling an external unknown perturbation to a known system. We show that our method produces exact synchronization with the given time series only when the trial function has a form identical to that of the perturbation.

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Anil Maybhate, R. E. Amritkar. 2000-02-17. Dynamic Algorithm for Parameter Estimation and Its Applications. https://doi.org/10.1103/physreve.61.6461

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