Adaptive control for a class of high-order nonlinear systems with unknown control coefficients and zero dynamics

This paper focuses on the adaptive stabilization problem for a class of high-order nonlinear systems with uncertain control coefficients and unmeasurable zero dynamics. Restriction on zero dynamics is further relaxed, and the dynamic order of a continuous adaptive state-feedback controller reduces to be minimum (only one dimension) through delicately defining an appropriate unknown parameters. 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. The designed controller guarantees all the closed-loop system states are globally uniformly bounded, and the original state converges to zero.