Optimization of source parameters in transport networks

This study centers on optimizing parameters related to concentrated sources that impact the functioning of transport networks. The transport network is composed of multiple one-dimensional objects, each following by a system of ordinary differential equations with nonlocal boundary conditions to characterize their states. The sources exert influence on specific points within these objects and their connection points. The goal of the optimization process is to identify the best locations and power levels for these sources, guided by predefined criteria for target functional. We establish the necessary optimality conditions for the parameters of concentrated sources.