< p>Chaos is a nonlinear behavior that shows chaotic and irregular responses to internal and external stimuli in dynamic systems. Chaos appears in the system which is very sensitive to initial condition. Study of chaos dynamic systems has quickly spread in the last three decades, and it has become a very attractive area of research to remove dynamic chaotic behaviors and make nonlinear systems stable. Stabilization has been considered as a high usage tool to eliminate aberrant behaviors of chaotic system and can be divided into two categories, regulation and tracking. In regulation stabilizing, system becomes stable by designing proper control signals to one of the available balance points or one of the alternate unstable paths on strange absorbers in chaos system. Another set of chaos systems stabilizing is tracking. In this type of stabilization, a reference signal varying with time and a control frame are considered in the way the system responses follow that signal. In this thesis, both regulation and tracking stabilizing are considered, first without chaos and then with chaos. For this purpose, smart and powerful adaptive neuro fuzzy inference system (ANFIS) technic is used. The proposed method is examined by a famous example of a chaos system called the Lorenz system. The simulation results show the ability of the proposed method. Our proposed approach is ANFIS which is designed for Lorenz chaotic system. it is compare with PID controller in the system .
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