Global Stabilization of Minimum Phase Nonlinear Systems with Unknown Virtual Control Coefficients

The problem of global stabilization via state feedback is studied for a class of linearizable minimum-phase nonlinear systems with uncertainties. In the case where the disturbance signals represent only an unknown constant vector parameter and appear linearly in the system, an adaptive controller is developed, to achieve global stability with state regulation. When the virtual control coefficients are also unknown for systems with trivial zero dynamics, the global stabilization is also achieved by adaptive scheme. In this paper, we considered a class of partially linearizable minimum-phase nonlinear system with unknown virtual control coefficients, having nontrivial zero dynamics. We used tuning functions design to reduce the dynamic order of the adaptive controller to its minimum, and achieved global asymptotic stability and tracking.