A continuous feedback approach to global strong stabilization of nonlinear systems
A continuous feedback approach to global strong stabilization of nonlinear systems
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DOI：
10.1109/9.935058
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发表时间：
2001-07-01
影响因子：
6.8
通讯作者：
Lin, W
中科院分区：
文献类型：
--
作者：
Qian, CJ;Lin, W
在本文中，我们提出了一个连续的反馈方法来解决问题的全局强稳定，真正的非线性系统，可能不会稳定，即使是局部的，任何光滑的反馈。我们描述的条件下，它是可能的证明，而没有光滑的控制器存在，存在的连续状态反馈控制律，实现全局强稳定性（GSS）的意义上的Kurzweil，证明是建设性的，并通过开发一个机器，它结合了齐次系统的理论与增加一个功率积分器的想法，全局稳定连续控制器的显式构造。然后，我们说明，通过例子，这种机制可以用来克服光滑反馈所造成的拓扑障碍，从而导致新的解决方案，以各种开放的控制问题，包括全球稳定的欠驱动不稳定的两个自由度的机械系统。
We present in this paper a continuous feedback approach to the problem of global strong stabilization, for genuinely nonlinear systems that may not be stabilized, even locally, by any smooth feedback. We describe conditions under which it is possible to prove, while no smooth controllers exist, the existence of continuous state feedback control laws that achieve global strong stability (GSS) in the sense of Kurzweil, The proof is constructive and carried out by developing a machinery, which combines the theory of homogeneous systems with the idea of adding a power integrator, for the explicit construction of globally stabilizing continuous controllers. We then illustrate, by means of examples, how this machinery can be used to overcome the topological obstruction caused by smooth feedback, and hence resulting in new solutions to a variety of open control problems, including global stabilization of an underactuated unstable two degree of freedom mechanical system.