This study considers optimization problems for time-varying network topologies that maximize the controllability of linear network systems under sparsity constraints. The major theoretical differences from the existing findings on control node scheduling problems is that our method is based on the matrix-valued Pontryagin maximum principle applied to the controllability Lyapunov differential equation. This allows us to handle various controllability metrics that can only be approximated by existing methods. Finally, we perform a numerical evaluation of our proposed method and compare results with those of our previous approximation method.

中文翻译：

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稀疏约束下可控性度量最大化的矩阵 Pontryagin 原理方法

本研究考虑时变网络拓扑的优化问题，在稀疏约束下最大化线性网络系统的可控性。与控制节点调度问题现有研究结果的主要理论差异在于，我们的方法基于应用于可控性 Lyapunov 微分方程的矩阵值 Pontryagin 极大值原理。这使我们能够处理只能通过现有方法近似的各种可控性指标。最后，我们对我们提出的方法进行数值评估，并将结果与​​我们之前的近似方法的结果进行比较。