Many networked systems built upon real-life physical or social interactions have time-varying connections among individual units, where the temporal changes in connectivity and/or interaction strength lead to complicated dynamics. The temporal network model was proposed in the form of controlled linear dynamical systems acting in an ordered sequence of time intervals. One of the core challenges in network science is the control of networks and the optimization of the control strategy. However, most canonical frameworks for solving optimal control problems were established for static networks featuring constant topology. New theories and techniques are yet to be developed for the temporal networks, with an important case being that the input and the source-node connection are both variables. In this work, by formulating a quadratic energy cost without solving the Riccati differential equation, we show that the control effort can be reduced substantially by improving either the system trajectories or the input matrices. The two approaches are further combined in a coordinate descent framework, integrating linearly constrained quadratic programming, and a projected gradient descent method. Taken together, the results underline the potential of temporal networks as energy-efficient control systems and present strategies to improve the control input. Moreover, the proposed algorithms can serve as a starting point for future engineering of real-world temporal networks.

中文翻译：

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具有可变输入和Node__source连接的时态网络的最优控制


许多建立在现实生活中的物理或社会交互基础上的网络系统在各个单元之间具有随时间变化的连接，其中连接和/或交互强度的时间变化导致复杂的动态。时间网络模型是以按时间间隔的有序序列起作用的受控线性动力系统的形式提出的。网络科学的核心挑战之一是网络的控制和控制策略的优化。然而，大多数解决最优控制问题的规范框架都是针对具有恒定拓扑的静态网络建立的。时间网络尚未开发新的理论和技术，一个重要的情况是输入和源节点连接都是变量。在这项工作中，通过在不求解 Riccati 微分方程的情况下制定二次能量成本，我们表明可以通过改进系统轨迹或输入矩阵来大幅减少控制工作。这两种方法进一步结合在坐标下降框架中，集成线性约束二次规划和投影梯度下降方法。总而言之，结果强调了时间网络作为节能控制系统的潜力，并提出了改进控制输入的策略。此外，所提出的算法可以作为现实世界时间网络未来工程的起点。