Optimal Nodal Control Of Networked Systems Of Conservation Laws

我们认为2x2系统的守恒定律在一个空间维度上的网络所产生的，例如，在管道网络中的气流和水流的网络中的明渠的建模。黎曼问题中的耦合条件的陈述允许不连续的解决方案。结果被用来设计适当的和自适应的数值方案，通过利用底层网络结构来解决优化和控制问题，即使是复杂的网络。

We consider 2x2 systems of conservation laws in one space dimension on networks arising for example in the modelling of gas flow in pipeline networks and water flows in networks of open channels. The statement of coupling conditions in terms of Riemann problems allows for discontinuous solutions. The results are used to design appropriate and adaptive numerical schemes by exploiting the underlying network structure to solve optimization and control issues even for complex networks.