Study On Identification Of Fractional-order Chaos System Withtiem Delay Based On Intelligent Algorithms

Chaos is a special kind of nonlinear system, which has a great deal of application potential, especially in data encryption, security communication, biomedical engineering and such engineering fields. With the development and improvement of chaos theory, its research methods trend to quantitative analysis. Either chaos control or chaos synchronization can be implemented under the conditon that the mathematical model of chaos system is achieved. So how to obtain the mathematics model of chaos system is of vital importance. In recent years, with the development of fractional calculus theory, frcational-order chaos has became a hot research issue. Fractional-order chaotic system has more complex dynamic characterristics than integer-order chaotic system, which can reflect the physical features of real systems in a better way. So research of frcational-order chaotic system owns more practical values. This dissertation focus on the identification issue of fractional-order chaotic system with time delay. Research methods involve intelligent optimization algorithms and fuzzy identification theory. The main study contents are as follows:Firstly, the research background and significance of this topic are given, including development process of chaos theory, development process of fractional calculus, research status of fractional-order chaos system and summary of intelligent optimization algorithms. Then the research status of chaos system identification is presented in the end.Secondly, the basic knowledge of fractional calculus is present. A numerical algorithm for fractional differential equation with time delay based on predictor-corrector method is proposed, which lays the mathematics foundation of the following research.Thirdly, an improved multi-select differential evolution algorithm is proposed, which balances the global search and convergence speed well. And it’s applied to parameters identification of fractional-order chaos system wtih time delay. Estimated parameters include fractional order, time delay and other parameters.Finally, fuzzy indetification of fractional-order chaos system with time delay is studied. An improved particle swarm optimization with random-perturbation is proposed and applied to optimize the T-S fuzzy model parameters. Simulation shows the proposed method can well approximate the fractional-order chaos system with time delay.