n this paper, an optimal backstepping controller is designed using particle swarm optimization with passive congregation (PSOPC) algorithm for controlling the chaos of Coullet chaotic system. The backstepping method consists of parameters with positive values. The parameters are usually chosen optional by trial and error method. The improper selection of the parameters causes improper system performance. The proposed optimal backstepping controller determines the parameters automatically,

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... igently and without trial and error by minimizing the integral of time multiplied absolute error (ITAE) and squared control signal using PSOPC Algorithm. By this new controller, the fastest response is achieved with the least control effort, i.e. the system chaos is controlled in the least time and with the lowest energy. Finally, the effectiveness of the proposed controller is shown by the control of chaos of Coullet chaotic system.