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 proposed for estimation of unknown bounds and adaptive control of the uncertain nonlinear system. To carry out the backstepping design with the estimation 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 on the Lyapunov function has a dead zone, whose size depends on the flat zone. The design procedure follows the standard backstepping with variations in dealing with the cross terms between different stages and the bound estimation. The stability analysis shows that all the variables of the closed-loop control system are bounded, and the output tracking error converges to the flat zone which can be arbitrarily small. The proposed method does not need any bound of uncertain parameters or unknown disturbances, and it prevents the bursting phenomena.