The Research On Control Of Chaotic Maps

Chaos appears irregular and unstable, whose behavior is complex but not random in deterministic systems. Chaos control is very popular research topic in the present. In this paper, the chaos controller is designed by use of feedback control to achieve the purpose of controlling chaos, based on Lyapunov exponent and discrete system stability criterion. By the way, Lyapunov exponent is an indicator of judging chaos. The main contributions of the research work presented in this dissertation are as follows:1. A feedback controller, which makes the periodic orbits of mapping reconstruct inside, is designed to control Logistic map to approach any desired stability targets including odd orbits in the chaos area based on discrete system stability criterion. This control method applies not only to low periodic orbits, but also to the higher periodic orbits.2. The original bifurcation characteristics of coupled logistic map will be changed when one uses a usual chaos controller. For this reason, the control of delaying and previa bifurcations is effectively realized by using the state variables feedback and parameter variation in this paper. Furtherly, chaotic control and anti-control of coupled logistic map is easily realized only by choosing the appropriate control parameters, without changing the original bifurcation characteristics of the system.3. BP neural network is used to design of chaos controller whose output is disturbance signal to achieve the purpose of controlling chaos becaues of the advantage of network. It can approximate a complex nonlinear function in arbitrary accuracy, has strong robustness and fault tolerance, massively parallelism, can study and adapt to the serious dynamic characteristics of uncertain systems.