The Stabilization Problem Of Nonholonomic Systems

In this paper, the stabilization problem of nonholonomic systems is discussed. Firstly, the robust adaptive control problem for a class of nonholonomic systems with nonlinear parameter is discussed. By the parameter separation technique, we translate the nonlinear parameter into linear parameter to design an adaptive control law which can guarantee that all the signals in the closed-loop are uniform ultimate boundedness and the system states are convergent to a small neighborhood of zero. Secondly, the stabilization problem of chained systems with unknown time-delay is discussed. By appropriate Lyapunov-Krasovskii function, the control law is constructed which can guarantee the closed-loop systems stable. Finally, a new design scheme of robust adaptive fuzzy control for a class of uncertain high order nonholonomic systems with strong nonlinear drifts is provided. The design is based on the approximation capability of fuzzy systems. Uniform ultimate boundedness of all the signals in the closed-loop are guaranteed, and the states are convergent to a small neighborhood of zero.