Adaptive robust backstepping design for a class of nonlinear system

Owing to the actual systems usually suffer the influence of disturbances, many robust design methods have been utilized to deal with the disturbance effects. In this paper, for a class of nonlinear system with internal and external disturbances, the storage functions of this kinds of system are constructed via integrating nonlinear L₂ gain disturbances attenuation theory smoothly into backstepping design methodology, and a novel nonlinear adaptive robust controller and parameter update law are obtained simultaneously. The construction procedure of both feedback control law and associated storage functions is systematic and concise. The theory analyses and simulation example demonstrate that the controller designed by this methodology possesses superior performances, because the derived controller dose guarantee the system states remains strictly bounded in close loop, and the disturbances effects on system output remains well attenuation too.