Design and Simulation of Adaptive Neuro Fuzzy Inference Based Controller for Chaotic Lorenz System

Chaos is a nonlinear behavior that shows chaotic and irregular responses to internal and external stimuli in dynamic systems. This behavior usually appears in systems that are highly sensitive to initial condition. In these systems, stabilization is a highly considerable tool for eliminating aberrant behaviors. In this paper, the problem of stabilization and tracking the chaos are investigated. In fact, this problem can be divided into two categories, regulation and tracking. These kinds of stabilization have been studied, first regardless of the chaos and then considering the chaos. For this purpose, smart and powerful adaptive neuro fuzzy inference system (ANFIS) technique is used because intelligent approaches unlike the classical methods do not require complex mathematical equations and do not need to acquire the dynamics. Moreover, ANFIS is a complete and optimized fuzzy approach that has both advantages of neural network and fuzzy network. Furthermore, it can acquire fuzzy membership functions automatically. The proposed technique is examined by a famous example of a chaos system called Lorenz system. The simulation results show the ability of the proposed technique and its effectiveness in comparison with PID controller in the system.