Abstract
Among various nonlinear systems, parameter identification of chaotic systems turns out to be a very challenging task because of their complex and unpredictable nature. The control and synchronization of chaotic systems remains incomplete until the parameters of the chaotic systems are known. Traditionally, the trend has been to estimate the parameters using gradient based search methods which suffer from premature convergence and trapping in local minima. This chapter presents an optimization based scheme for estimation of the parameters of two chaotic systems namely Lorenz and Rossler, using two recently developed bio-inspired optimization algorithms, i.e. cuckoo search algorithm (CSA) and flower pollination algorithm (FPA). CSA is based on mimicking the breeding behavior and hostile reproduction strategies of cuckoo with the effective use of levy flight for providing global optimization while FPA is based on the natural process of flowering plants due to self and cross pollination using both levy flight strategies for global convergence and random walk for local convergence. The performance of these optimization algorithms, for efficient estimation of the parameters of chaotic system, is compared in terms of the resulting integral of absolute error (IAE). Simulation results demonstrated the effectiveness of CSA in offline 3D parameter estimation of the considered two chaotic systems over the FPA. The minimum fitness offered by FPA is 2.4E-03 and 5.03E-06 and by CSA it is 7.92E-06 and 1.31E-07 for the parameter estimation of the 3D Lorenz and Rossler chaotic system, respectively.