Adaptive chattering free variable structure control for a class of chaotic systems with unknown bounded uncertainties

A new adaptive control scheme is developed for a class of chaotic systems with unknown bounded uncertainties. It is implemented by using variable structure control. The concept of extended systems is used such that continuous control input is obtained to avoid chattering phenomenon as frequently in the conventional variable structure systems. Furthermore, it is worthy of note that the proposed adaptive control scheme does not involve any information about the bounds of uncertainties. Thus, the limitation of knowing the bounds of uncertainties in advance is certainly released. A numerical simulation is included to verify the validity of the developed adaptive chattering free variable structure control.