Stabilization of Navier-Stokes Flows
Stabilization of Navier-Stokes Flows
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DOI：
10.1007/978-0-85729-043-4_3
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发表时间：
2010-11
期刊：
影响因子：
--
通讯作者：
V. Barbu
中科院分区：
文献类型：
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作者：
V. Barbu
在本章中，我们讨论纳维-斯托克斯方程的平稳（平衡）解的反馈稳定性。鲁棒稳定反馈控制的设计是抑制流体动力学中发生的不稳定性和湍流的主要方法，我们在内部控制器和边界控制器的情况下处理这个问题。第一个案例已经在第 1 章的抽象背景中介绍过。 2，控制器分布在空间域中，并且具有任意小的紧凑支持。第二种情况是控制器集中在边界上。在这两种情况下，我们设计了一个鲁棒且具有有限维结构的可稳定反馈线性控制器，即，它是相应线性化系统的特征函数的线性组合。从控制理论的角度来看，这意味着驱动虽然是无限维的，但仅限于边界的任意子域。
In this chapter we discuss the feedback stabilization of stationary (equilibrium) solutions to Navier–Stokes equations. The design of a robust stabilizing feedback control is the principal way to suppress instabilities and turbulence occurring in the dynamics of the fluid and we treat this problem in the case of internal and boundary controllers. The first case, already presented in an abstract setting in Chap. 2, is that in which the controller is distributed in a spatial domainand has compact support taken arbitrarily small. The second case is that where the controller is concentrated on the boundary. In both cases, we design a stabilizable feedback linear controller which is robust and has a finite-dimensional structure, that is, it is a linear combination of eigenfunctions for the corresponding linearized systems. From the control theory point of view, this means that the actuation, though infinite-dimensional, is confined to an arbitrary subdomainor to the boundary.