Parameter Estimation for One-Dimensional Chaotic Systems by Guaranteed Algorithm and Particle Swarm Optimization

The problem of parameter estimation is considered for chaotic systems described by one-dimensional discrete maps. The article presents a two-stage estimation technique that combines the ideas of guaranteed (set-membership) approach and swarm intelligence. The first stage is the preprocessing of measurements by the guaranteed algorithm. The result of the guaranteed estimation is interval estimates of the unknown variables (the initial condition and parameter of the chaotic map). The second stage is the minimization of the cost function using particle swarm optimization. The previously computed interval estimates define the set of possible values of the cost function arguments. It decreases the number of local minima of the cost function and improves the convergence of the optimization algorithm. The proposed estimation technique is useful in the case of a small number of available measurements. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.