Adaptive control of chaotic systems based on a single layer neural network

Prediction based chaos control via a new neural network

“…First, an approximate period orbit is obtained, where the period is T and the sampling interval is T s . The method to obtain the approximate period orbit is similar as the method in reference [10]. Suppose T can be divided exactly by T s .…”

“…If chaos prediction can be made around the unstable fixed point, an improvement is available on the second step. In our recent research [10], the dynamic of the chaotic system around the unstable fixed point is predicted by a single layer neural network. Then the control input can eliminate the errors not only on the unstable direction but also on the stable direction.…”

Nonlinear feedback control on single-species chaotic model with harvesting coefficient

“…A series of chaos control method have been put forward such as OGY method [9], hybrid control of chaos [10],delay feedback control method [11], linear stability of the methods, adaptive control method [12], fuzzy control methods [13]. Consider a one-dimensional nonlinear system where x n denotes state variables of system, a is a system parameter and the value of a makes (7) keep in a chaotic state.…”

“…We apply the continuous nonlinear feedback control method to make become stable, Under controlled conditions, system equation of the one-dimensional mapping (12) can be described as…”

Controlling hyperchaos in hyperchaotic Lorenz system using feedback controllers

“…Recently, controlling this kind of complex dynamical systems has attracted a great deal of attention within the engineering society. Research efforts have investigated the chaos control in many physical chaotic systems [2][3][4][5][6][7][8][9][10][11][12][13]. Recently, following the pioneer work of Ott et al [2], different control strategies for stabilizing chaos have been proposed, such as Adaptive variable structure control [14], feedback control [15], and LMI approach [16].…”