Nonlinear feedback stabilization of a two-dimensional Burgers equation
Nonlinear feedback stabilization of a two-dimensional Burgers equation
复制标题
二维 Burgers 方程的非线性反馈稳定性
DOI：
10.1051/cocv/2009028
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
J. Raymond
中科院分区：
文献类型：
--
作者：
Laetitia Thevenet;J. Buchot;J. Raymond
本文研究了二维Burgers方程通过非线性反馈边界控制绕定常解的稳定性。我们感兴趣的是Dirichlet和Neumann边界控制。在文献中，它已经表明，线性控制律，确定稳定的线性化方程，局部稳定的二维Burgers方程。在本文中，我们定义了一个非线性控制律，也提供了一个局部指数稳定的二维Burgers方程。最后，我们用几个数值模拟，比较性能的非线性法律的线性。
In this paper, we study the stabilization of a two-dimensional Burgers equation around a stationary solution by a nonlinear feedback boundary control. We are interested in Dirichlet and Neumann boundary controls. In the literature, it has already been shown that a linear control law, determined by stabilizing the linearized equation, locally stabilizes the two-dimensional Burgers equation. In this paper, we define a nonlinear control law which also provides a local exponential stabilization of the two-dimensional Burgers equation. We end this paper with a few numerical simulations, comparing the performance of the nonlinear law with the linear one.