Indiscernible topological variations in DAE networks
Indiscernible topological variations in DAE networks
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DOI：
10.1016/j.automatica.2018.12.012
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发表时间：
2019-03
期刊：
影响因子：
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通讯作者：
Deepak U. Patil;P. Tesi;Stephan Trenn
中科院分区：
文献类型：
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作者：
Deepak U. Patil;P. Tesi;Stephan Trenn
讨论了微分代数方程（DAE）网络中拓扑变化不可检测的特征条件。它表明，初始条件的拓扑变化是不可辨别的属于一个广义本征空间共享的名义系统和系统的拓扑变化。一个条件的名义系统的特征向量推导出检查存在的可能无法辨别的拓扑变化。对于齐次网络，这个条件简化为具有相等分量的网络的拉普拉斯算子的特征向量的存在。最后，推导出一个秩条件，它可以用来检查拓扑变化是否保持标称网络的正则性。
A problem of characterizing conditions under which a topological change in a network of differential–algebraic equations (DAEs) can go undetected is considered. It is shown that initial conditions for which topological changes are indiscernible belong to a generalized eigenspace shared by the nominal system and the system resulting from a topological change. A condition in terms of eigenvectors of the nominal system is derived to check for existence of possibly indiscernible topological changes. For homogeneous networks this condition simplifies to the existence of an eigenvector of the Laplacian of network having equal components. Lastly, a rank condition is derived which can be used to check if a topological change preserves regularity of the nominal network.