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

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.

Fast chaotic optimization algorithm based on locally averaged strategy and multifold chaotic attractor

“…Application of chaos in industrial and applied problems is a very important and urgent research topic [1][2][3][4][5] . In particulary in theory of control, cryptography and more recently in global optimization algorithms where introduction of chaotic numbers instead of random ones leads to better results [6]. In general, chaos has three main dynamics properties [7]: sensitive dependence on initial conditions assessed by Lyapunov exponents [8][9][10], stochasticity and ergodicity.…”