Genetic Algorithms Theory And The Application In Parameter Estimation Of Time Delay System

Genetic algorithm is a kind of imitating life algorithm in macroscopy, which take the generation and evolution course of all the life and intelligence as the imitative mechanism. Through imitating the principle of Darwin's the theory of biological evolution, it stimulate good structure; through imitating Mendel's the theory of genetic variation, it keep existing structure in the course of iteration and seek better structure. Genetic algorithm has some good character such as simple, applicable, strong robustness. More over, this method can realize total search and applies to parallel disposal, so it has been used in function optimization, combination optimization, system identification, pattern identification and intelligence control system. However, with the application and research much limitation of genetic algorithm has been exposed. In this paper, we give a deep research into the basic theory of genetic algorithm about some problem having to be settled urgently and give a kind of its application in parameter estimation of time-varging-delay system.Firstly, the general model of binary genetic algorithm and the pattern theorem are introduced. We also explain the limitation and the basic limit theorem of finite Markov chain, which has nothing to do with initial time. At the same time, the convergence of genetic algorithm is analyzed and the relation among the convergence definitions is obtained by analyzing restricted condition in convergence definition.Secondly, the mathematical model of time-delay system, which is delay differential equation, is introduced. From the properties of delay differential equation and genetic algorithm, we give a kind of disposal method aboutmathematical model when having time delay parameter estimation about time-varying-delay system by using genetic algorithm. Furthermore, a kind of common method about time delay parameter estimation of time-varying-delay system basing on genetic algorithm is proposed. In the same chapter, the advantage of this method is theoretically proved. Moreover, combining with the movement model of wavy ship affected by storm and through emulation, the validity of this method is also proved.Thirdly, considering that genetic algorithm theory lack exactitude, which result from the lack of exactitude of operator's description, in this paper, we proceed from the field of definitions, the range and operation mode and give a deep analysis into select operator, crossover operator and mutation operator. At the same time, the definition of operator's consistency is given and the narrow operator is defined by operator with consistency, which make genetic algorithm theory stricter and make the system more integrated. Furthermore, the effect of different operators on pattern living number is analyzed and the stricter proof of pattern theorem is given.Lastly, taking coding space as the subject, some definitions of coding subspace are given and cardinality theory of coding space is established. Attainable probability of subset of coding space is also defined and using cardinality as a tool, the limitation of search ability of crossover operator and the necessity of the existence of mutation operator are proved by analyzing attainable probability. At the same time, the direct sum decomposition of coding space is briefly introduced and a kind of direct sum decomposition method taking crossover attainability as equivalent condition is given.