Time-delay chaotic systems have some very interesting properties, and their parameter estimation has received increasing interest in the recent years. It is well known that parameter estimation of a chaotic system is a nonlinear, multivariable, and multimodal optimization problem for which global optimization techniques are required in order to avoid local minima. In this work, a seeker-optimization-algorithm (SOA)-based method is proposed to address this issue. In the SOA, search direction is based on the empirical gradients by evaluating the response to the position changes, and step length is based on uncertainty reasoning by using a simple fuzzy rule. The performance of the algorithm is evaluated on two typical test systems. Moreover, two state-of-the-art algorithms (i.e., particle swarm optimization and differential evolution) are also considered for comparison. The simulation results show that the proposed algorithm is better than or at least as good as the other two algorithms and can effectively solve the parameter estimation problem of time-delay chaotic systems.

• Received 12 April 2010

DOI:https://doi.org/10.1103/PhysRevE.83.036203