Global finite-time adaptive stabilization for nonlinear systems with multiple unknown control directions

In this paper, the problem of global finite-time stabilization is addressed for a class of nonlinear systems with multiple unknown control directions. Unlike all the existing works on finite-time stabilization, our work allows the control directions of the considered systems to be unknown. This paper is the first to focus on the global finite-time control of such uncertain systems. To overcome the main obstacle arising from unknown control directions, we develop a novel Lyapunov-based logic switching rule, and then the desired adaptive switching controllers are designed, where the controller parameters are to be tuned online in a switching manner according to the proposed switching logic. It is shown that the obtained controllers guarantee the closed-loop systems being globally finite-time stable. A simulation example is provided to illustrate the effectiveness of the proposed control algorithms.