Adaptive Robust control of Hyperchaotic Rossler system in the presence of matching disturbance

This paper deals with the problem of adaptive robust control based on Lyapunov theory for uncertain feedback linearizable systems with matching uncertainties. The proposed method shows that the closed-loop system is globally asymptotically stable; and states of the system track the desired trajectories in a globally asymptotically manner. Since this approach is not concerned with any information about the bounds of uncertainties, the preliminary knowledge of the bounds of uncertainties is not nessary. Next, in order to prevent the switching phenomenon in the control signal, the method is modified such that the norm of tracking error will be Uniformly Ultimately Bounded. Numerical simulations on the hyperchaotic Rossler system with matching disturbance show fast responses in set-point tracking, while norm of the errors is certainly bounded and the control signal is reasonably smooth.