Robust Controlling Chaos for Unified Chaotic Systems via Sliding Mode Control

Robust Synchronization of Unified Chaotic Systems via Adaptive Sliding Mode Control

“…The parameter law is shown as Figure 3. As can be seen from these results, the proposed adaptive sliding mode controller (11) works well and the synchronization errors can converge to zero at fast speed. Figure 4 is the simulations results corresponding to the states of drive-response systems with.…”

“…Remark2.1. The nonlinear functions are assumed uncertain in drive-response systems, which are different from other unified chaotic system in reference [4,[6][7][8]11], so adaptive law of the sliding mode controller is designed basic on the unknown Lipschitz constants of uncertain nonlinear functions, which is different from the other proposed adaptive sliding mode control. So the designing method in this paper has some advantages than other sliding mode controller.…”

“…So, it is necessary to explore the synchronization of the uncertain unified chaotic systems. In the past decades, many studies have been conducted to investigate the synchronization of unified chaotic systems [4,[6][7][8][9][10][11][12]P . Up to dates, many effective control methods for chaotic synchronization have been proposed, such as active control [12]P , impulsive control [13]P , nonlinear and linear control [14,15]P , adaptive control [4,7,16]P , and so on.…”

“…Up to dates, many effective control methods for chaotic synchronization have been proposed, such as active control [12]P , impulsive control [13]P , nonlinear and linear control [14,15]P , adaptive control [4,7,16]P , and so on. In many practical engineering, lots of chaotic systems are inches advantages such as fast response, good transient performance, and insensitive to variation or external disturbances, so sliding mode controller is adopted in stabilization or synchronization of chaotic systems widely [8,11,16]. However, the nonlinear function in drive-response system is known in this reference.…”