Adaptive Output Feedback for a Class of Three-order Nonlinear Systems with Unknown Control Directions

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.