Adaptive feedback control of nonlinear time-delay systems: the LaSalle-Razumikhin-based approach
Adaptive feedback control of nonlinear time-delay systems: the LaSalle-Razumikhin-based approach
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DOI：
10.1109/tac.2005.854652
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发表时间：
2005-11
影响因子：
6.8
通讯作者：
Xiaohong Jiao;T. Shen
中科院分区：
文献类型：
--
作者：
Xiaohong Jiao;T. Shen
提出了一种非线性时滞系统自适应反馈控制器设计的新方法。首先，利用LaSalle-Razumikhin定理，得到了一类泛函微分方程部分解稳定收敛的充分条件.然后，利用这个条件，解决了非线性时滞系统的自适应镇定问题。对于一类具有三角形结构的非线性时滞系统，通过递归构造Lyapunov-Razumikhin函数，可以得到自适应镇定控制器.它将表明，所提供的递归设计方法，这显然是由典型的反推方法的动机，是不是一个平凡的扩展现有的设计方法。
This note presents a new method to design adaptive feedback controller for nonlinear time-delay systems. First, by using the LaSalle-Razumikhin theorem, a sufficient condition is derived that ensures the convergence of a part of the solution with stability for a class of functional differential equations. Then, using this condition, the adaptive stabilization problem is solved for nonlinear time-delay systems. Moreover, it is shown that for a class of nonlinear time-delay systems with triangular structure the adaptive stabilizing controller can be obtained by recursively constructing the Lyapunov-Razumikhin function. It will be shown that the provided recursive design approach, which is obviously motivated by the typical backstepping method, is not a trivial extension of the existing design method.