Research On Swarm Intelligence Optimization Algorithms And Their Applications To Parameter Identification Of Fractional-order Systems

Swarm intelligence optimization algorithms are a kind of stochastic optimization algorithms generated by simulating the intelligent behaviors of the natural biological population,and they have characteristics like the low requirement for objective functions and independent on the selection of initial starting points.Thus,these algorithms have provided highly effective solutions for optimization problems from different fields.Up to now,a lot of new or enhanced swarm intelligence optimization algorithms have been proposed,among which the performances of some algorithms are validated not only in theoretical research but also in practical application.However,there is still room for improvement in many aspects of the research on swarm intelligence optimization algorithms.For example,how to achieve a fine balance between exploration and exploitation abilities is still a problem worthy of discussion.Besides,some algorithms reveal disadvantages such as low accuracy,slow convergence speed,or easy to fall into local optimum when applied to certain practical problems.Hence,it is necessary and significant to put forward improved algorithms.Besides,most of the existing swarm intelligence optimization algorithms are usually designed for a specific problem.When considering the other different types of problems,these algorithms may have a risk of ineffectiveness.So only studying problem-specific algorithms is limited,and it is quite important to utilize benchmark functions with different complex characteristics to evaluate the optimization performance of the algorithms comprehensively.On the other hand,researches on parameter identification of fractional-order systems is of great significance in the field of control and synchronization of nonlinear systems.Parameter identification of fractional-order systems can be converted to a multi-dimensional optimization problem by establishing the corresponding mathematical model.Because of the introduction of fractional differential operator and the complexity of nonlinear systems,the constructed fitness function may contain multiple local extremum points.The traditional optimization algorithms cannot handle it,also the original swarm intelligent optimization algorithms cannot obtain satisfactory results.Therefore,putting forward improved swarm intelligent optimization algorithms are quite necessary.Based on the above discussions,this thesis mainly studied one kind of swarm intelligence optimization algorithms represented by cuckoo search(CS),and proposed a series of improved swarm intelligence optimization algorithms by analyzing the characteristics and shortcomings of the algorithm.The proposed algorithms are applied to the problem of parameter identification of integer-order and fractional-order systems.Furthermore,the function optimization problems with higher application value and broader application scope are considered in order to evaluate the performance of the proposed algorithms.The main contents of the thesis are as follows:(1)Parameter identification of integer-order nonlinear systems based on a hybrid cuckoo search algorithm.The local search phase of the original cuckoo search algorithm adopts a simple random walk rule,the search speed of which is fast,but it has low diversity of solutions.In order to improve the search ability of the local search phase,an effective hybrid cuckoo search(HCS)algorithm is proposed by introducing the concepts of differential evolution and opposition-based learning.To verify the effectiveness of the proposed algorithm,HCS is applied to identify the unknown parameters of integer-order chaotic systems with and without time delays.The experimental results show that HCS can search for more accurate estimated values at a faster speed.What's more,additional experiments are conducted to test the validity of the improved parts in HCS.Accordingly,two HCS variants are considered: CS-IDE and CS-OBL.After tests,it can be concluded that both the two improved parts contribute to the improvement of parameter identification results.Also,CS-IDE and CS-OBL are shown competitive when compared with other algorithms.(2)Parameter identification of fractional-order nonlinear systems based on an improved quantum-behaved particle swarm optimization algorithm.The original quantumbehaved particle swarm optimization(QPSO)is easy to fall into the local optimum,but it has advantages such as quick convergence rate and few controls parameters needed to adjust.To simultaneously improve the shortcomings and retain the advantages of QPSO,an improved QPSO algorithm(namely IQPSO)is proposed by using the fitnessbased mean best position,generalized opposition-based learning,and differential evolution operator.The proposed IQPSO algorithm is applied to the problem of parameter identification of fractional-order chaotic systems,where both fractional orders and systematic parameters are treated as unknown parameters to be identified.Moreover,the influence of noises on parameter identification is also considered.Therefore,this work is more challenging to deal with compared with the previous research.By analyzing the experimental results,IQPSO can be considered as a method with high accuracy,strong generality,and good robustness for the problem of parameter identification of fractional-order nonlinear systems,and shows superiority over other algorithms.(3)Function optimization based on two improved cuckoo search algorithms and their applications.Through the study of parameter identification of fractional-order systems,we find that swarm intelligence optimization algorithms designed for specific problems often have certain limitations,and only show their advantages in some specific problems.Consequently,based on the previous work,the function optimization problems are used.Meanwhile,to further improve the optimization performance of CS,two improved CS algorithms with good effectiveness and wide generality are proposed:a novel cuckoo search algorithm under adaptive parameter control(namely CSAPC),and an adaptive cuckoo search algorithm with optional external archive(namely ACSOEA).In order to test the two algorithms comprehensively,two test suites are used,including 48 benchmark functions with different complex properties such as unimodal,multimodal,rotated and/or shifted.Furthermore,the proposed algorithms are applied to identify the unknown parameters of fractional-order systems.The experimental results demonstrate that both CSAPC and ACS-OEA have high calculation accuracy and convergence efficiency,and they can be applied to diverse practical problems from different areas.(4)Analysis of probability distribution functions in cuckoo search algorithm.For algorithms,its exploration ability is closely related to the random numbers generated by some given distribution functions.CS uses L?evy flights based on the L?evy heavytailed distribution,both mean and variance of which is infinite,thus CS can always search for a wider area within the feasible region,which has a great impact on enhancing its search efficiency.Nonetheless,different heavy-tailed distributions may also improve the search ability of CS to some extent.Therefore,the influence of different heavy-tailed distributions on CS is discussed.Four typical heavy-tailed distributions are respectively introduced to CS,and accordingly,four modified CS algorithms with different heavy-tailed distributions are proposed.The experimental results show that the modified CS algorithms can obtain better results than CS in most cases.