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A global adaptive output-feedback control scheme is proposed for a class of nonlinear system in output-feedback form with additive output derivative. Unknown parameters are allowed to multiply not only the output nonlinearities but also affine functions of the derivative of the measured output with coefficients that are smooth nonlinear functions of the measured output. Through coordinate transformation and parameter redefinition, the system considered is transformed into the parametric output-feedback canonical form with unknown high-frequency gain sign. To tackle this situation, Nussbaum gain is incorporated in the adaptive backstepping technique. Tuning function method is employed to design the parameter adaptive law to avoid overparametrization. All the signals involved in the closed-loop system can be guaranteed globally uniformly bounded and the asymptotic tracking is achieved. The results of this paper extend the class of uncertain nonlinear systems for which global adaptive output-feedback control can be designed.

A global adaptive output-feedback control scheme is proposed for a class of third-order relative degree nonlinear system with unknown control directions and affine additive output derivative. Trough parameter-dependent coordinate transformation and parameter redefinition, the system considered is transformed into the parametric output-feedback form with known output functions as the virtual control gain functions. To tackle the situation that the unknown high frequency gain sign, Nussbaum gain is incorporated in the adaptive backstepping technique. Tuning function method is employed to design the parameter adaptive law to avoid overparametrization. The closed-loop system can be guaranteed all the signals involved globally uniformly bounded and asymptotic tracking is achieved. The result of this paper enlarges the class of uncertain nonlinear systems for which global adaptive output-feedback control can be designed.