L. Guessas∗ and K. Benmahammed∗
Backstepping design, chaotic system, Lyapunov function, control law, asymptotic stability
A simple control law based on the theory of backstepping is proposed to control and track a Lorenz chaotic system to any desired trajectory. The backstepping design is a step-by-step approach and consists of a recursive procedure, interlacing the choice of a Lyapunov function with the design of a virtual control at each step; at the last step, the true control is obtained. Strong properties of global and asymptotic stability can be achieved. A major advantage of this method is that, it has the flexibility to build the control law by avoiding cancellations of useful nonlinearities.
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