A Class Of Improved Artificial Bee Colony Algorithm For Unknown Parameter Estimation Of Fractional-order Nonlinear Systems

It is an important issue to estimate unknown parameters of fractional-order non-linear systems, which is of vital significance and has received increasing attentions in the fields of computational mathematics and nonlinear science. The parameter estima-tion problem can be transformed into a multi-dimensional optimization problem via a functional extreme value model. And many kinds of intelligent optimization algorithm have been applied to solve this optimization problem. In particular, the artificial been colony (ABC) algorithm is a competitive population-based intelligent optimization al-gorithm which has many wonderful properties. Due to its easy implementation and quick convergence, nowadays, the ABC algorithm has received a lot of attentions and wide applications in different continuous optimization problems. However, as far as we know, for the parameter estimation of uncertain fractional-order nonlinear systems, little research has been done through the ABC algorithm. On the other hand, so far, there has been no specific algorithm to achieve the best solution for all optimization problems. Namely, as far as most algorithms are concerned, it is difficult to simul-taneously balance the ability of exploitation and exploration for all the optimization problems. Therefore, in this paper, to further enhance the exploration and the exploita-tion abilities, three kinds of improved ABC algorithms are proposed, and then they are respectively applied to estimate the unknown parameters of fractional-order nonlinear chaotic and hyperchaotic systems. The main contributions and original ideas included in the dissertation are summarized as follows:1. The solution searching equation in the original ABC algorithm is good at ex-ploration but poor at exploitation. Therefore, to keep the ability of exploitation and exploration well balanced, a modified ABC algorithm (named MABC) is proposed. In the proposed MABC algorithm, two new searching equations are proposed to generate the new candidate solutions by considering the global best solution of the previous it-eration. Experiments are conducted on two typical fractional-order nonlinear chaotic systems to show the effectiveness of the proposed scheme. It is shown that, for the given parameter configurations and maximum number of iterations, the modified ABC algorithm could estimate the unknown fractional orders and parameters of the uncer-tain fractional-order nonlinear chaotic systems more rapidly, more accurately and more stably than other algorithms.2. In order to enhance the global convergence, when producing the initial popu-lation and scout bees, both chaotic system and opposition-based learning method are employed. In addition, the ratio between employed and onlooker bees is changed to have a better searching performance. Then a hybrid artificial bee colony (HABC) al-gorithm is proposed. The HABC algorithm is further used for parameter estimations of uncertain fractional-order nonlinear chaotic systems. As a result, compared to some ABC-based algorithms and other typical population-based algorithms, the simulation results demonstrate the good performance and the superiority of the HABC algorithm. Thus, it can be a promising candidate for parameter estimation of uncertain fractional-order chaotic systems.3. To further improve the exploration and the exploitation ability, a hybrid adaptive artificial bee colony algorithm combined with simulated annealing algorithm, called HABCSA, is put forward. In the HABCSA algorithm, two new searching equations with adaptive weight coefficient are proposed and the corresponding searching dimen-sion is modified at the same time. Besides, the simulated annealing (SA) operator is added to hybridize with the modified ABC algorithm. Then, the proposed HABCSA al-gorithm is applied to the parameter estimation of fractional-order arbitrary dimensional nonlinear hyperchaotic systems. Simulation results demonstrate that proposed hybrid algorithm is effective and comparative to estimate the unknown parameters when com-pared with some other typical population-based evolutionary algorithms.