二阶域论中边界条件和边界端口的提取
On the extraction of the boundary conditions and the boundary ports in second-order field theories
摘要：
在本文中，我们考虑在变分设置的二阶域论。根据变分原理，欧拉-拉格朗日方程以一种明确的方式遵循，但众所周知，这对于嘉当形式是不正确的。这也有后果时，允许在边界上的非平凡的变化的边界条件的推导。通过对可能的边界项的集合提出额外的条件，我们利用Cartan形式中的自由度来提取物理上有意义的边界表达式。将应用相同的数学机制来导出偏微分方程的哈密顿表示中的边界端口，这对于基于能量的控制方法是至关重要的。我们的结果将被可视化的机械系统，如梁和板模型。
英文摘要：
In this paper we consider second-order field theories in a variational setting. From the variational principle the Euler-Lagrange equations follow in an unambiguous way, but it is well known that this is not true for the Cartan form. This has also consequences on the derivation of the boundary conditions when non trivial variations are allowed on the boundary. By posing extra conditions on the set of possible boundary terms we exploit the degree of freedom in the Cartan form to extract physical meaningful boundary expressions. The same mathematical machinery will be applied to derive the boundary ports in a Hamiltonian representation of the partial differential equations which is crucial for energy based control approaches. Our results will be visualized for mechanical systems such as beam and plate models.
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