Design of robust controllers for uncertain chaotic systems with nonlinear inputs

A variable structure control (VSC) design for a class of uncertain chaotic systems subject to sector nonlinear inputs is considered in this paper. It is guaranteed that, under the proposed control law, chaotic systems can asymptotically drive the system orbits to arbitrarily desired trajectories even with both uncertainties and input nonlinearities. However, in the sliding mode, the investigated uncertain chaotic system with nonlinear input still possesses advantages of fast response, good transient performance and insensitive to the parameter uncertainties and external disturbances as the systems with linear input. A Duffing–Holmes system is used as an illustrative example to demonstrate the effectiveness of the proposed VSC design method.