A unified time-varying feedback approach and its applications in adaptive stabilization of high-order uncertain nonlinear systems

We are concerned with two key problems of adaptive control design: one is to find the feasible conditions and the valid boundary of the time-varying feedback scheme; another one lies in the improved generalization of the homogeneous idea in the global adaptive stabilization of high-order uncertain nonlinear systems. The distinguished feature of the system to be investigated is the serious coexistence between unknown time-varying parameters and unknown time-varying control coefficients. Design procedures of the continuous controller are provided based on the sign function technique and the delicate search of the time-varying function and a Lyapunov function. Finally, the control of uncertain single-link robotic manipulator demonstrates the application of design scheme.