Analysis and design of robust adaptive control for nonlinear output feedback systems under disturbances with unknown bounds

Robust adaptive control of nonlinear output feedback systems under bounded disturbances whose bounds are unknown is considered. A new algorithm is pro posed for estimation of unknown bounds and adaptive central of the uncertai n nonlinear system. To carry out the backstepping design with the estimatio n of unknown bounds, a new Lyapunov function is introduced with a flat zone in the pre-specified neighbourhood of the origin. The adaptive law based o n the Lyapunov function has a dead zone, whose size depends on the flat zon e. The design procedure follows the standard backstepping with variations i n dealing with the cross terms between different stages and the bound estim ation. The stability analysis shows that all the variables of the closed-lo op control system are bounded, and the output tracking error converges to t he flat zone which can be arbitrarily small. The proposed method does not n eed any bound of uncertain parameters or unknown disturbances, and it preve nts the bursting phenomena.