Finite-Time Control using Locally Semiconcave Control Lyapunov Function for Differentially Flat Systems

The design of control Lyapunov functions (CLFs) for guaranteeing finite-time stability is a difficult problem. In this paper, we propose a finite-time controller design method by using locally semiconcave CLF (LS-CLF) for differentially flat systems. The LS-CLF is composed of two CLFs: a global CLF obtained by the minimum projection method for an original system and a homogeneous CLF for a homogeneous system at the origin. Then, a discontinuous state feedback controller that finite-time stabilizes the origin of the original system is obtained. The effectiveness of the proposed method is confirmed by computer simulation for a trajectory tracking control problem of a two-wheeled mobile robot.