Finite-time VFO Stabilizers for the Unicycle with Constrained Control Input

Introduction

In the recent years, the problem of finite-time convergence for the continuous dynamic systems has attracted more attention of the researchers [1, 4, 2]. On one hand, accomplishing the stabilization control task in a finite time seems to be more natural from a practical point of view than the infinite-time solution characteristic for the classical asymptotic results. On the other hand, as presented in [1], the finite-time stable systems are more robust, guaranteeing improved rejection of the non-vanishing (persistent) low-level disturbances. Moreover, the continuous finite-time stabilizers make it possible to avoid the so-called chattering phenomenon intrinsic for example for low-order sliding mode controllers. Utilization of the finite-time stability results in the control design for mobile robots can have an additional merit coming from the possibility of assessing the settling time interval in the closed-loop system. It can facilitate the motion planning stage.