We study the well-posedness of a class of dynamical flow network systems describing the dynamical mass balance among a finite number of cells exchanging flow of traffic between themselves and with the external environment. Dynamical systems in the considered class are described as differential inclusions whereby the routing matrix is constant and the outflow from each cell in the network is limited by a control that is a Lipschitz continuous function of the state of the network. This framework finds application in particular within traffic signal control, whereby it is common that an empty queue can be allowed to have more outflow than vehicles in the queue. While models for this scenario have previously been presented for open-loop outflow controls, our result ensures the existence and uniqueness of solutions for the network flow dynamics in the case Lipschitz continuous feedback controllers.

我们研究了一类动态流网络系统的适定性，描述了有限数量的细胞之间的动态质量平衡，它们在它们之间以及与外部环境之间交换了流量。所考虑类别中的动态系统被描述为差分包含，其中路由矩阵是恒定的，并且网络中每个单元的流出受到网络状态的 Lipschitz 连续函数的控制的限制。该框架特别适用于交通信号控制，因此通常可以允许空队列比队列中的车辆有更多的流出。虽然此场景的模型之前已针对开环流出控制提出过，