Fast finite-time adaptive stabilization of high-order uncertain nonlinear systems with output constraint and zero dynamics

This paper investigates the problem of fast finite-time adaptive stabilization for a class of high-order uncertain nonlinear systems with an output constraint and zero dynamics. A continuous stabilizer with an adaptive mechanism is constructed by utilizing a tangent function and a serial of nonnegative integral functions equipped with sign functions, which guarantees the system output to be restricted in a pre-specified region and a faster convergence speed of system states compared to traditional finite-time stabilizers. The main novelty of this paper is the skillful selection of Lyapunov functions and the new perspective of constructing a fast finite-time adaptive stabilizer with the consideration of output constraints as well as dynamic and parameter uncertainties. A simple example is given to demonstrate the effectiveness of the proposed strategy.