The use of evolutionary optimization techniques such as genetic algorithms, differential evolution, swarm optimization and genetic programming to solve the inverse problem of parameter estimation for nonlinear chaotic systems has been gaining popularity in recent years. The efficacy of such evolutionary schemes depends on the definition of a suitable fitness function which is used to compare potential solutions in the population. In almost all research involving evolutionary schemes for parameter identification, displacement values of the first few hundred Poincaré points, after ignoring transient effects, have been used as the feature set. The measured response of the system is compared to the response of the potential solutions in the population over these Poincaré points, although there is no empirical research to show that such a feature set works better than other possible feature sets. In this paper, a smaller feature set based on first and second-order statistical parameters of the response are considered and the estimation results are compared to the estimate produced by using the standard Poincaré points-based feature set, called the finite sample feature set in this paper. Also compared are results using three evolutionary algorithms — firefly algorithm, particle swarm optimization and differential evolution. It has been shown that the proposed feature set converges to a near-optimal solution faster and in fewer generations and produces estimates that are comparable to those obtained with the finite sample feature set.
Parameter estimation for chaotic systems based on hybrid differential evolution algorithm
