Study On Biogeography-Based Optimization For Parameters Estimation And Control Of Chaotic Systems

As optimization problems exist widely in fields of nonlinear science and engineering practice,for example,control and synchronization of chaotic systems etal,the study of the problems has its substantial theoretical significance and actual value.With its strong robustness,excellent diversity and parallelism,biogeography-based optimization(abbr.BBO)which can simulate migration,mutation and extinction of species in biogeography is fit for working the problems out.With their increasing complexity of uncertainty,strong nonlinearity and time variation,it is not easy to fulfil their demands on its performance with a single optimization scheme.Hybrid BBO can bring forward them new ideas and effectual way.For the sake of conquering these problems,a few methods are put forward better BBO's exploration capability and quicken its convergence speed.The major study work is as follows.1.A revised BBO with ring topology and Powell's schemes,abbr.RPBBO,is proposed to solving parameters estimation of discrete chaotic systems.Firstly,a hybrid migration operator is constucted by substituting global topology for ring one.Secondly,a new mutation operator is adopted for remedying the deficiencies of the original one and then intergrated into BBO for picking up its convergence speed.Lastly,numerical simulations for Logistic and H é non chaotic systems identification show the effectiveness of the proposed method.2.A modified BBO with random perturbation and differential mutation,abbr.PDBBO,is proposed to solving parameters estimation of continues chaotic systems.Firstly,a hybrid migration operator is designed by fusion of improved differential mutation strategy and previous migration operator,which can utilize more information with both old migration operator and mutation ways.Secondly,a stochastic perturbation operator is embedded into BBO for improving population diversity and enhancing exploration ability.Lastly,numerical simulation and comparisons are carried out based on some typical chaotic systems,including Lorenz system,Chen system and Lü system.Experimental results display that PDBBO's performance is more splendid than the others.3.The parameter estimation problem for time-delay chaotic system is formulated as a multi-dimensional optimization problem by treating the time delay as an additional parameter.A modified BBO with orthogonal crossover,abbr.ODBBO,is put forward figuring the problem out.Firstly,a revised migration operator is raised by replacing original migration operator with differential mutation operator for improving population diversity.Secondly,orthogonal crossover can search both boundary and inner of their fessible region at the same time.Hence,orthogonal crossover is embedded into BBO for making up the shortage of migration operator and heightening its exploration capability.Finally,the performance of the proposed ODBBO is compared with the other state-of-the-art algorithms in terms of parameter accuracy and computational time.The simulation results show that the proposed algorithm is better than or at least as good as the other algorithms and can effectively solve the parameter estimation problem of time-delay chaotic systems.4.That is still an insufficiency in BBO regarding its migration operator,which is good at exploitation but poor at exploration.To address this concerning issue,an improved BBO(CGBBO)is presented by using a modified search strategy to generate a new mutation operator in order that the exploration and exploitation can be well balanced and then satisfactory optimization performances can be achieved.In addition,to enhance the global convergence,both opposition-based learning method and chaotic maps are employed,when producing the initial population.The proposed algorithm is applied to control and synchronization of Hénon systems which can be formulated as high-dimension numerical optimization problems with multiple local optima.Numerical simulations and comparisons with some typical existing algorithms demonstrate the effectiveness and efficiency of the proposed approach.5.Aiming at the discrete nonlinear minimax problems with each component being convex function,biogeography-based optimization-proximal point algorithm,abbr.PPBBO,is presented.By using smoothing function,minimax problem is transformed into the unconstrained optimization problem of smooth function.The algorithm employs the proximal point algorithm as the outer algorithm,and the biogeography based optimization as the internal algorithm.The numerical experiments show that the hybrid algorithm has the advantage of the fine stability,fast convergence speed and high precision,and it is an effective algorithm for nonlinear minimax problems.