Chaos suppression of a class of unknown uncertain chaotic systems via single input

This paper deals with the design of a robust adaptive control scheme for chaos suppression of a class of chaotic systems. We assume that model uncertainties and external disturbances disturb the system’s dynamics. The bounds of both model uncertainties and external disturbances are assumed to be unknown in advance. Moreover, it is assumed that the nonlinear terms of the chaotic system dynamics are unknown bounded. Based on the global boundedness feature of the chaotic systems’ trajectories, a simple one input adaptive sliding mode control approach is proposed to suppress the chaos of the uncertain chaotic system. Furthermore, using a dynamical sliding manifold the discontinuous sign function in the control input is diverted to the first derivative of the control input to eliminate the chattering. Finally, the robustness of the proposed approach is mathematically proved and numerically illustrated.