The Finite-Time Stabilization Problem Of Nonholonomie Systems

In this paper, we discussed the nonholonomic systems, and discussed the finite-time stabilization problems of the systems. First of all, adaptive finite-time control is presented for a class of uncertain nonholonomic systems in chained form with nonlinear parameterization. Using parameter separation, state scaling and backstepping, an adaptive finite-time control law is obtained in the form of continuous time-invariant feedback. Both Lyapunov stability and finite time convergence are guaranteed by appropriately choosing the design parameters. An adaptive control based switching strategy is used to overcome the uncontrollability problem associated with x0(t0)=0. Simulation example demonstrates the effectiveness and the robust features of the proposed controller.Furthermore, the paper investigates the problem of finite-time stabilization for a class of stochastic nonholonomic systems in chained form. By using stochastic finite-time stability theorem and the method of adding a power integrator, a recursive controller design procedure in the stochastic setting is developed. Based on switching strategy to overcome the uncontrollability problem associated with x0(0)=0, global stochastic finite-time regulation of the closed-loop system states is achieved. The proposed scheme can be applied to the finite-time control of nonholonomic mobile robot subject to stochastic disturbances.The simulation results show the effectiveness of the presented algorithm.