Adaptive control for a class of uncertain time delay chaotic systems with unknown control direction

In this paper, a new observer-based backstepping output control design is proposed for controlling a general class of uncertain time-delay chaotic systems. A state observer is utilized to estimate the system states with unknown control direction. The control direction is detected based on the Nussbaum-type function and adaptive backstepping output feedback control is constructed without requiring a priori knowledge of the signs of the control directions, which can achieve output tracking. It is shown that proposed controller are able to guarantee semi globally uniform ultimate boundedness of all signals in the closed loop systems. Finally, the proposed methods are applied to chaotic systems to verify the effectiveness of the proposed method.