Abstarct: In this thesis, the benefits of the adaptive fuzzy and PID control with performance are used to chaos control. To this end, an adaptive fuzzy PID with tracking performance is studied. To compensate the uncertainties, we used the comprehensive approximation capability of fuzzy and tracking performance for reduce approximation error. Stability and robustness of the proposed control scheme are proved baxsed on Lyapunov approach and modified Riccuti-like equation. The results show the superiority of the proposed control method in chaos control of duffing oscillator. Moreover, in order to achieve optimal performance of the proposed controller, its parameters are obtained using optimization algorithms such as Particle Swarm Optimal, Genetic Algorithm and a new algorithm namely Backtracking Search optimization. The results are compared together. Simulation results demonstrate the capability of the proposed controller in robusttracking performance.