Adaptive backstepping control of uncertain Lorenz system

In this paper, a novel robust adaptive control method is proposed for controlling the well-known Lorenz chaotic attractor. Firstly, we design a new Backstepping controller for controlling the Lorenz system based on the Lyapunov stability theorem. The proposed method is different from the typical Backstepping control method and it can overcome the singularity problem appeared in using the typical Backstepping control method. So by exploiting the property of the system, the resulting controller is singularity free and the closed-loop system is stable globally. Since in practice we have not access to full information of the system states, we set the controller parameters in order to achieve a controller form which only needs to one system state. To overcome the problem of parameter uncertainty we add a term to Lyapunov function and obtain an identification law to have a negative definite Lyapunov function derivative. Simulation results demonstrate the effectiveness of the proposed approaches.