Finite-time stabilization with arbitrarily prescribed settling-time for uncertain nonlinear systems

Abstract

This paper considers global finite-time stabilization with arbitrarily prescribed settling-time for nonlinear systems with unknown control directions and other serious uncertainties. In view of the challenge of the problem and the scarcity of available methods, several motivating facts are offered by elaborating examples and counterexamples. The facts disclose the potential obstructions in pursuing continuous controllers and force us to resort to powerful discontinuous feedbacks. By combining the method of adding a power integrator, homogeneous approach and desingularization technique, a state-feedback controller with design parameters is first proposed. Then a switching logic is proposed to tune the parameters online, wherein two types of switching sequences are involved to suppress serious uncertainties and to guarantee arbitrarily prescribed settling-time, respectively. Also, fixed-time stabilization is considered as a special case, aiming at the trade-off between arbitrary rapidness and high control cost. Two examples are provided to demonstrate the effectiveness of the proposed strategy.