Finite-time stabilization of high order nonholonomic systems in power chained form

In this paper, a finite-time control strategy is presented for a class of high order nonholonomic systems in power chained form with strong nonlinear drifts. The robust control laws are developed by the use of input-state-scaling and adding a power integrator backstepping technique. Based on switching strategy to overcome the uncontrollability problem associated with x₀(0) = 0, the solution of the resulting closed-loop system is globally finite-time regulated at origin.