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首页> 外文期刊>IEEE Transactions on Automatic Control >Controllability and Observability of Grid Graphs via Reduction and Symmetries
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Controllability and Observability of Grid Graphs via Reduction and Symmetries

机译：通过归约和对称性控制网格图的可控性和可观察性

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摘要

In this paper, we investigate the controllability and observability properties of a family of linear dynamical systems, whose structure is induced by the Laplacian of a grid graph. This analysis is motivated by several applications in network control and estimation, quantum computation and discretization of partial differential equations. Specifically, we characterize the structure of the grid eigenvectors by means of suitable decompositions of the graph. For each eigenvalue, based on its multiplicity and on suitable symmetries of the corresponding eigenvectors, we provide necessary and sufficient conditions to characterize all and only the nodes from which the induced dynamical system is controllable (observable). We discuss the proposed criteria and show, through suitable examples, how such criteria reduce the complexity of the controllability (respectively, observability) analysis of the grid.
机译：在本文中，我们研究了线性动力学系统族的可控性和可观察性，该系统的结构是由网格图的拉普拉斯算子引起的。这种分析是由网络控制和估计，量子计算和偏微分方程离散化中的几种应用推动的。具体来说，我们通过图的适当分解来表征网格特征向量的结构。对于每个特征值，基于其多重性和相应特征向量的适当对称性，我们提供必要和充分的条件来表征所有且仅特征点，从该节点可以控制（观察到）动力学系统。我们讨论了提出的标准，并通过适当的示例显示了这些标准如何降低网格的可控性（分别为可观察性）分析的复杂性。

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