On long-term boundedness of Galerkin models
On long-term boundedness of Galerkin models
复制标题
DOI：
10.1017/jfm.2014.736
复制
发表时间：
2013-09
影响因子：
3.7
通讯作者：
M. Schlegel;B. R. Noack
中科院分区：
文献类型：
--
作者：
M. Schlegel;B. R. Noack
摘要研究了具有能量保持二次项的线性二次动力系统。这些系统例如作为不可压缩流的伽辽金系统而出现。给出了系统动力学长期有界性的判据。如果违反该准则，则对于有效的非线性，不存在全局稳定的吸引子。因此，该标准可以被认为是面向控制的Galerkin模型的粘性流体流动的最低要求。该标准举例说明，例如，Galerkin系统的二维缸尾流模型在瞬态和后瞬态制度，洛伦兹系统和壁有界剪切流。该判据有许多潜在的应用，例如，强非线性动力系统的系统降阶和控制。
Abstract We investigate linear–quadratic dynamical systems with energy-preserving quadratic terms. These systems arise for instance as Galerkin systems of incompressible flows. A criterion is presented to ensure long-term boundedness of the system dynamics. If the criterion is violated, a globally stable attractor cannot exist for an effective nonlinearity. Thus, the criterion can be considered a minimum requirement for control-oriented Galerkin models of viscous fluid flows. The criterion is exemplified, for example, for Galerkin systems of two-dimensional cylinder wake flow models in the transient and the post-transient regime, for the Lorenz system and for wall-bounded shear flows. There are numerous potential applications of the criterion, for instance, system reduction and control of strongly nonlinear dynamical systems.