Research On Evolutionary Algorithms For Chaos Systems Parameter Estimation And Control

So many scientists are being infatuated with the enigma of creation mechanism of turbulence in several centuries, which was named the last puzzle of the classical Physics. But researches on turbulence are not progressing smoothly and remain at the level of half experience and immature theory. In which the fundamental Navier-Stokes equation for the fluid and plasma is regarded as one of the seven greatest hard nuts to crack in Parisian international mathematics conference for 21 centuries in 2000.Investigating the enigma of creation mechanism of turbulence from chaos provides s novel way of thinking and the new approach for uncovering the enigma and control the turbulence, and it is attached great importance both in domestic and abroad now. Up to now lots of valid methods have been put forward to chaos control and synchronization. These not only provide necessary approach for the applications of chaos theory but also promote the thorough study in theories of chaos and fluid mechanics especially in turbulence.The deep investigations and studies in chaos' unknown system parameters estimation and higher order unstable periodic orbits (UPO) and related algorithms will exert a deep influence on both chaos control and chaotic characteristics based on UPO. However, the limitations of the existing algorithms, such as methods in Newton kind, in detecting UPO and estimating system parameters online and the developments and demands of chaos control and synchronization form a sharp contrast.In view of above mentioned reasons, the simplified model of Navier-Stokes equation Lorenz chaos system and their reducing in 2 dimensions Henon system is considered in unknown parameter estimation, control and synchronization. Through appropriate functions' minimizations of correspondent models transforming, the proposed evolutionary algorithms recent achievements Differential Evolution (DE) and Particle Swarm Optimization (PSO) with the proper improvements are adopted. The rest of this paper is organized as follows.In Chapter 1, we introduce the research background and meaning of chaos firstly. Then the history and current situation of the chaos system related to turbulence, multi-phase flows and Navier-Stokes equation are probed and analyzed. Thirdly the main aspects, the key problems to be solved and the main innovations we have researched are introduced.