Modified dynamic minimization algorithm for parameter estimation of chaotic system from a time series

Nonlinear Dynamics (Impact Factor: 3.01). 01/2011; 66(1):213-229. DOI: 10.1007/s11071-010-9922-0

ABSTRACT This paper proposes a modified dynamic minimization algorithm for parameter estimation of chaotic systems, based on a scalar
time series. Comparing with the previous design proposed by Maybhate and Amritkar (Phys. Rev. E 59:284–293, 1999), two important new design concepts related to the feedback control and the auxiliary functions for parametric updating laws
are introduced. Two different types of estimates can then be derived, and numerical simulations confirm their superior performances
to the designs based on the original dynamic minimization algorithm or other existing approaches. Furthermore, a circuit experiment
is carried out to demonstrate the robustness and practicability of the proposed design.

KeywordsChaotic systems–Dynamic minimization–Darameter estimation–Synchronization

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    ABSTRACT: A method for estimating model parameters based on chaotic system response data is described. This estimation problem is made challenging by sensitive dependence to initial conditions. The standard maximum likelihood estimation method is practically infeasible due to the non-smooth nature of the likelihood function. We bypass the problem by introducing an alternative, smoother function that admits a better-defined maximum and show that the parameters that maximize this new function are asymptotically equivalent to maximum likelihood estimates. We use simulations to explore the influence of noise and available data on model Duffing and Lorenz oscillators. We then apply the approach to experimental data from a chaotic Duffing system. Our method does not require estimation of initial conditions and parameter estimates may be obtained even when system dynamics have been estimated from a delay embedding.
    Nonlinear Dynamics 70(1). · 3.01 Impact Factor