Parameter estimation for chaotic system based on evolution algorithm with hybrid crossover

Abstract

A hybrid-crossover-based evolution algorithm is proposed to estimate the parameters of chaotic system. Through establishing an appropriate fitness function, the parameter estimation problem is coverted into a multi-dimensional functional optimization problem. In this approach, the individual generation based on good-point-set method is introduced into the evolutionary algorithm initial step, which reinforces the stability and global exploration ability of the evolutionary algorithm. In the evolution process, it not only can be explored to induce the new individuals generated by stochastic hybrid crossover operation to fly into the better subspace, but also can avoid the premature convergence and speed up the convergence. It coordinates the exploitation ability and the exploration ability of algorithm. Numerical simulations on the benchmark function and the Lorenz system are conducted. The results demonstrate the effectiveness of the proposed algorithm, which is shown to be an effective method of parameter estimation for chaotic systems.