Circuit Simulation And Control Of Chaotic Systems

In 1960s, E. N. Lorenz firstly discovered chaotic attractor in numerical experiment, from then on; chaos theory has been obtained huge, far-reaching development in many fields. A great deal investigation shows that relation between chaos and engineering technology has been become closer. Chaos has far-ranging applied foreground in many fields such as biological engineering, electronic engineering, chemical engineering, information engineering, application mathematics and experimental physics and so on. Owing to excessive complexity of chaotic systems, people consider it was impossible to control chaos at all times. Yet, in 1990, Ott,Grebogi and Yorke proposed a concept for controlling chaotic systems which successfully carried out control of chaotic systems, henceforth, the study of controlling chaos caught the attention.Firstly, definition of chaotic system, how to produce chaos, and chaotic features were introduced, and several controlling chaos methods, realization way of chaos control and applied research survey were briefly elaborated.Then, the nonlinear dynamical nature of chaotic systems was studied, strange attractors were observed by graphics simulation and numerical simulation, basic principle to design chaotic circuit by operational amplifier, resistor and capacitor was analyzed, and a new method to design chaotic circuit by operational amplifier, resistor and capacitor was proposed.Finally, the problem of stable controlling Lorenz chaotic system was studied, using T-S fuzzy model as an approximation for nonlinear chaotic system, the nonlinear chaotic system was fuzzy into local linear model, and the controller designed by using stability theory insures the stability of T-S fuzzy system, and parameters of fuzzy controller were regard as controller's parameters of nonlinear systems under control to control chaotic systems. The effect of the scheme was tested by simulation.