Robust chaotic control of Lorenz system by backstepping design

This work presents a robust chaotic control strategy for the Lorenz chaos via backstepping design. Backstepping technique is a systematic tool of control law design to provide Lyapunov stability. The concept of extended system is used such that a continuous sliding mode control (SMC) effort is generated using backstepping scheme. In the proposed control algorithm, an adaptation law is applied to estimate the system parameter and the SMC offers the robustness to model uncertainties and external disturbances so that the asymptotical convergence of tracking error can be achieved. Regarding the SMC, an equivalent control algorithm is chosen based on the selection of Lyapunov stability criterion during backstepping approach. The converging rate of error state is relative to the corresponding dynamics of sliding surface. Numerical simulations demonstrate its advantages to a regulation problem and an orbit tracking problem of the Lorenz chaos.