Global output-feedback adaptive stabilization for uncertain nonlinear systems with polynomial growth nonlinearities

In this paper, the problem of global adaptive stabilization by smooth output-feedback is investigated for a class of uncertain nonlinear system with unmeasured states dependent growth. The highlight of the paper lies in that the growth rate with output-dependent polynomial growth and the measurement sensitivity are both unknown, or the dimension of the closed-loop system is significantly reduced. To handle these, a distinct observer with two high-gains is introduced and two dynamic high-gains are updated in the new forms. Motivated by the closely related works, we propose a systematic non-identifier based output feedback control scheme by using the idea of universal control and backstepping technique. The designed controller can globally regulate the states of the original system and the observer while maintaining global boundedness of the closed-loop system. A numerical example is given to demonstrate the effectiveness of the proposed method.