不变流形在非完整链式系统镇定中的应用

该文研究了非完整链式系统的反馈镇定问题.针对非完整链式系统,构造了给定控制律下系统的不变流形,基于所构造的不变流形,提出了一种反馈镇定控制律的求解方法,并利用该方法求得了一个非连续时不变反馈控制律及控制律参数选择的充分必要条件,证明了所得控制律能使n维非完整链式系统各状态指数收敛于原点,求得了在该控制律作用下,非完整链式系统各状态的解析解.最后,利用仿真示例验证了所提控制律的有效性.

Application of Invariant Manifolds in Stabilization of Nonholonomic Chained Form Systems

This paper studies the feedback stabilization of nonholonomic chained form system. Aimed at the nonholonomic chained form system, the invariant manifold under the given controller is constructed. Based on the invariant manifold, a solution to make a feedback stabilization controller is proposed, and a discontinuous time-invariant feedback controller and the necessary and sufficient conditions that the parameters select are obtained. This paper proves that the n-dimensional nonholonomic chained system can be stabilized to the origin exponentially by the proposed controller. The analytical solution of every state under the proposed controller is calculated. Finally, the simulation result shows the effectiveness of the proposed controller.