Monotonicity of actuated flows on dissipative transport networks
Monotonicity of actuated flows on dissipative transport networks
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耗散传输网络上驱动流的单调性
DOI：
10.1109/ecc.2016.7810392
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
M. Chertkov
中科院分区：
文献类型：
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作者：
Anatoly Zlotnik;Sidhant Misra;Marc Vuffray;M. Chertkov
我们得到了商品在整个网络中传输的一般瞬变流的单调性性质，其中该流是由在结点具有密度连续性和质量平衡条件的边上的密度和质量流动力学来表征的。每条边上的动力学由一个一般的偏微分方程组表示，该偏微分方程组近似于具有能量耗散的亚音速可压缩流体流动。转移的商品可以在任何节点注入或取出，并由位于节点的压缩机在整个网络中推进。这些压缩机是可控制的执行器，提供了一种通过网络操纵流量的方法，因此我们将其视为控制系统。一个典型的问题需要选择压缩机控制方案，以便在优化经济或运行成本目标的同时，提供时变的节点商品退出曲线，并且密度保持在严格的限制内。在这篇手稿中，我们考虑了这样一种情况，其中每个节点的商品退出轮廓是不确定的，但在已知的最大和最小依赖于时间的限制内是有界的。引入了单调参数控制系统的性质，并证明了一般的动态耗散网络流在一定条件下具有这一性质。这一性质有助于非常有效地描述这类系统的最优控制问题，其中解对于商品退出的不确定性必须是鲁棒的。我们讨论了几个应用，在这些应用中，出现了这样的控制问题，其中单调性能够简化系统行为的表征。
We derive a monotonicity property for general, transient flows of a commodity transferred throughout a network, where the flow is characterized by density and mass flux dynamics on the edges with density continuity and mass balance conditions at the nodes. The dynamics on each edge are represented by a general system of partial differential equations that approximates subsonic compressible fluid flow with energy dissipation. The transferred commodity may be injected or withdrawn at any of the nodes, and is propelled throughout the network by nodally located compressors. These compressors are controllable actuators that provide a means to manipulate flows through the network, which we therefore consider as a control system. A canonical problem requires compressor control protocols to be chosen such that time-varying nodal commodity withdrawal profiles are delivered and the density remains within strict limits while an economic or operational cost objective is optimized. In this manuscript, we consider the situation where each nodal commodity withdrawal profile is uncertain, but is bounded within known maximum and minimum time-dependent limits. We introduce the monotone parameterized control system property, and prove that general dynamic dissipative network flows possess this characteristic under certain conditions. This property facilitates very efficient formulation of optimal control problems for such systems in which the solutions must be robust with respect to commodity withdrawal uncertainty. We discuss several applications in which such control problems arise and where monotonicity enables simplified characterization of system behavior.