Abstract: This paper studies the robust adaptive output-feedback control problem for a class of nonlinear cascade systems with unknown control directions. The original system with unknown directions is firstly transformed into a new system without unknown control direction by using the linear transformation. Then, based on the linear high gains observer and Nussbaum function, a novel robust adaptive output-feedback controller is proposed. Furthermore, it is proved that all the closed-loop signals remain bounded and the states asymptotically converge to the origin under the controller. Furthermore, a sufficient condition for the asymptotic stability of the closed-loop system is derived by constructing a new Lyapunov function. Finally, a simulation example is given to illustrate the effectiveness of the proposed control laws.

Key words: nonlinear cascade systems, output-feedback, adaptive control, unknown control direction