L1 adaptive control for a class of uncertain nonlinear systems based on observer

A novel L1 adaptive control strategy based on a sliding mode observer using a back-stepping design method for a class of uncertain nonlinear systems in a strict block feedback form is presented. Due to the incompletely observable system states, a sliding mode observer is designed to estimate system states, and the convergence is analyzed. Moreover, the ideal control law is derived through the back-stepping method. In order to overcome the terms explosion problem, a nonlinear tracking differentiator is used to extract differential signals of virtual control. In order to improve the transient performance of system response and eliminate the high-frequency chatter of the control input, the L1 adaptive control is introduced to improve the control laws and the stability of the system is proved. Finally, a numerical simulation is given to demonstrate expected performance of the proposed control scheme. ©, 2015, Chinese Institute of Electronics. All right reserved.