A Class Of Algorithm Design For Parameter Estimation Of Fractional-Order Nonlinear Systems

Recently,due to the global optimization,versatility and parallel processing capabil-ities,the intelligent optimization algorithm has received a lot of attention.We mainly studied and improved the artificial bee colony algorithm and the flower pollination algo-rithm.On the one hand,the artificial bee colony algorithm has the advantages of few parameters,simple structure and easy implementation.However,the artificial bee colony algorithm will encounter problems such as slow convergence speed,difficulty in balanc-ing exploration and exploitation ability in the later stage of the optimization process.In order to improve this situation,a modified artificial bee colony algorithm is proposed and applied to the estimation for unknown parameters of fractional-order nonlinear systems.On the other hand,the flower pollination algorithm has strong global optimization ability,but it is prone to premature phenomenon and the poor exploitation ability in the late stage of iteration.We modify it in three aspects and tested it with global optimization problem.The main work of this paper is as follows:1.In order to balance the exploitation and exploration ability of the artificial bee colony algorithm,a modified artificial bee colony algorithm is proposed.Firstly,initial-ization of population is the first step of the algorithm,and is also an important step,which is the basis and guarantee of the latter iteration.In order to get a better initial population,we apply a combination of chaos optimization algorithm and opposition-based learning method.Second,the search equations are the core of algorithm.Two new search equa-tions are used to balance exploitation and exploration ability.In addition,inspired by the Nelder-Mead simplex method,it is combined with the artificial bee colony algorithm to solve the problem of slow convergence speed in the late iteration.Finally,we choose two fractional-order chaotic systems for parameter estimation.The experimental results show that compared with other algorithms,the improved artificial bee colony algorithm has higher precision and faster convergence speed.2.In order to improve the slow convergence speed in the later stage of flower pol-lination algorithm,an adaptive flower pollination algorithm with memory is proposed.Similar to the artificial bee colony algorithm,we use a combination of chaos optimization algorithm and opposition-based learning method to generate the initial population.In ad-dition,the balance between global exploration and local exploitation in the algorithm is difficult,and the switching probability in the algorithm is the key to balance the two abil-ities.An adaptive probability mechanism is proposed,in which the switching probability is increased when the global search equation is better than the local equation,on the con-trary,the probability is reduced.This guarantee a large probability of global exploration in the early stage and a high possibility of local exploitation in the later stage.Besides,the memory of animals is considered,and most of the pollinators in the pollination phe-nomenon are animals or insects,thus memory mechanisms is designed in the algorithm.Finally,14 benchmark functions are selected to test the performance of the algorithms.The results show that the modified flower pollination algorithm can effectively improve the convergence speed.