Abstract
Parameter estimation for fractional-order chaotic systems has been an interesting and important issue in theory and various fields of application. In this paper, fractional orders, as well as systematic parameters of fractional-order chaotic systems are considered by treating fractional orders as additional parameters. The parameter estimation is transformed into a multidimensional optimization problem, and an effective modified artificial bee colony algorithm is proposed to solve this problem. Numerical simulations are conducted on two typical fractional-order chaotic systems to show the effectiveness of the proposed scheme.
Highlights
Considerable attention has been give to making use of the great potential of fractional calculus in physics [1], electrical circuit theory [2] and control systems [3]
The modified artificial bee colony (MABC) algorithm is further used to estimate the parameters of uncertain fractional-order chaotic systems via a functional extrema model
Algorithm, and the MABC algorithm proves to be a promising candidate for parameter estimation of uncertain fractional-order chaotic systems
Summary
Considerable attention has been give to making use of the great potential of fractional calculus in physics [1], electrical circuit theory [2] and control systems [3]. The ABC algorithm has only one control parameter (limit) apart from colony size and maximum cycle number. It uses less control parameters, the performance of the ABC algorithm is better than or similar to that of these algorithms, and it can be efficiently used for solving multimodal and multidimensional optimization problems. The MABC algorithm is further used to estimate the parameters of uncertain fractional-order chaotic systems via a functional extrema model. Numerical simulations are performed to estimate two well-known fractional-order chaotic systems and statistically compared with some typical existing methods. The simulation results demonstrate the good performance and the superiority of the MABC algorithm, and the MABC algorithm proves to be a promising candidate for parameter estimation of uncertain fractional-order chaotic systems.
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