有入流和流量分配控制的交汇处守恒律模型的optimization
On the optimization of conservation law models at a junction with inflow and flow distribution controls
摘要：
本文提出了一个分析网络上守恒律模型控制问题的一般框架。即我们考虑了一般的结点分布控制和流入控制，并建立了一类解的流迹在$L^1$中的紧性。然后，我们推导出两个最优化问题的解的存在性：（I）最大化的积分泛函取决于通量迹的解决方案评估的传入和传出的边缘的点;（II）最小化的全变差差的最优解的问题（I）。最后，我们提供了一个等价的变分制定的最小最大问题（II），我们讨论了一些数值模拟与两个传入和两个传出的边缘交界处。
英文摘要：
The paper proposes a general framework to analyze control problems for conservation law models on a network. Namely we consider a general class of junction distribution controls and inflow controls and we establish the compactness in $L^1$ of a class of flux-traces of solutions. We then derive the existence of solutions for two optimization problems: (I) the maximization of an integral functional depending on the flux-traces of solutions evaluated at points of the incoming and outgoing edges; (II) the minimization of the total variation of the optimal solutions of problem (I). Finally we provide an equivalent variational formulation of the min-max problem (II) and we discuss some numerical simulations for a junction with two incoming and two outgoing edges.
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