Global Adaptive Stabilization of High-order Nonlinear Systems with Zero Dynamics

This paper investigates the global adaptive stabilization for a class of high-order nonlinear systems with uncertain control coefficients and unmeasurable zero dynamics. Compared with the existing works, restriction on zero dynamics is further relaxed, and the dynamic order of a continuous adaptive state-feedback controller is reduced to be minimum (only one dimensional) through delicately defining an appropriate unknown parameter. The design procedures of the controller are provided by flexibly incorporating the method of adding a power integrator with the related adaptive technique and the idea of changing supply functions. Finally, a simple example is given to demonstrate the effectiveness of the control scheme.