An adaptive control scheme for recovering periodic motion of chaotic systems

The paper presents an adaptive control scheme for recovering the original dynamics of a nonlinear system after a sudden disturbance in a system parameter by controlling the system parameter through linear feedback. The key problem is to choose the control stiffness in the feedback by assigning the poles of the linearized controlled system in an extended state space, which consists of the system state and the system parameter. The paper gives the simulations of recovering the fixed point of the logistic map and the periodic orbit of a harmonically forced Duffing oscillator from the chaos due to a large disturbance in the parameter. The simulations demonstrate well the efficacy and the advantages of the proposed adaptive control scheme.