Monotonicity Properties of Physical Network Flows and Application to Robust Optimal Allocation
Monotonicity Properties of Physical Network Flows and Application to Robust Optimal Allocation
复制标题
物理网络流的单调性及其在鲁棒优化分配中的应用
DOI：
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发表时间：
2020
影响因子：
20.6
通讯作者：
Anatoly Zlotnik
中科院分区：
文献类型：
--
作者：
Sidhant Misra;Marc Vuffray;Anatoly Zlotnik
我们得到的条件单调性特性的特征一般流动的商品在网络上，其中的流动是由潜在的和流动的动态的边缘，以及潜在的连续性和克希霍夫-诺依曼质量平衡的要求在节点上。运输的商品可以在任何网络节点处注入或取出，并且其在整个网络中的移动由节点致动器控制。对于一类耗散的非线性抛物型偏微分方程（PDE）网络系统，我们得到了稳态流的单调性以及状态的单调序关于时变边界条件参数的传播条件.在后一种情况下，初始条件和时变参数的耦合条件在顶点提供了一个初始边值问题（IBVP）。我们证明了当初始条件和时变耦合律的参数适当时，IBVP的解的序性质被保持。然后，我们证明了当单调序不保持时，解的第一个交叉发生在网络节点。我们认为，鲁棒优化和最优控制配方和实时监测网络上的不确定动态流的影响，并讨论了物理网络上的能量耗散的亚音速可压缩流体流的应用。主要结果和监测政策的天然气管道测试网络和案例研究使用的数据对应于一个真实的工作系统。我们提出了应用这个一般结果的控制和监测的天然气输送网络。
We derive conditions for monotonicity properties that characterize general flows of a commodity over a network, where the flow is described by potential and flow dynamics on the edges, as well as potential continuity and the Kirchhoff–Neumann mass balance requirements at nodes. The transported commodity may be injected or withdrawn at any of the network nodes, and its movement throughout the network is controlled by nodal actuators. For a class of dissipative nonlinear parabolic partial differential equation (PDE) systems on networks, we derive conditions for monotonicity properties in steady-state flow, as well as for propagation of monotone ordering of states with respect to time-varying boundary condition parameters. In the latter case, initial conditions and time-varying parameters in the coupling conditions at vertices provide an initial boundary value problem (IBVP). We prove that ordering properties of the solution to the IBVP are preserved when the initial conditions and the parameters of the time-varying coupling law are appropriately ordered. Then, we prove that when monotone ordering is not preserved, the first crossing of solutions occurs at a network node. We consider the implications for robust optimization and optimal control formulations and real-time monitoring of uncertain dynamic flows on networks and discuss the application to subsonic compressible fluid flow with energy dissipation on physical networks. The main result and monitoring policy are demonstrated for gas pipeline test networks and a case study using data corresponding to a real working system. We propose applications of this general result to the control and monitoring of natural gas transmission networks.
影响因子：
2.1
作者：
Arioli M
通讯作者：
Arioli M
基于投影的生化网络模型简化第二部分：随机情况
DOI：
10.1109/cdc.2014.7039952
发表时间：
2014
期刊：
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影响因子：
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作者：
Sootla A
通讯作者：
Sootla A