Evolutionary modeling for parameter estimation for chaotic system

Abstract

On the basis of evolutionary algorithm, a novel method for parameter estimation of nonlinear dynamic equations is given in the present paper. Numerical tests indicate that the unknown parameters all can be estimated quickly and accurately whether the partial parameters are unknown or all parameters are unknown in the classic Lorenz equation. However, it is found that the convergence rate of the new algorithm is relatively slow when multiple unknown parameters are estimated simultaneously. To solve this problem, a corresponding improvement of measure is proposed, namely, a constraint mechanism is taken during the variation operation of evolutionary algorithm. The improvement is mainly based on the characteristic that the longer the running time of the evolutionary algorithm, the smaller the range of variation of the estimated parameters. Results indicate that the searching speed of the algorithm is greatly improved by using the improved estimation parameter project.