Some Results in Minimum–Time Optimal Control of Dynamical Flow Networks

Dynamical flow networks have emerged in the scientific community as a valuable tool to model the time-varying behavior of transportation and communication engineering systems. In this work, we present some results on the minimum-time optimal control of single-commodity dynamical flow networks, showing how it is possible to identify some structural properties relating optimality conditions and graph topology through a mathematical tool defined as the optimality matrix. Additionally, proving some results on the admissibility of solutions, which have significant implications for the activation of control inputs within the optimal time interval, leading to some derivations regarding the number of switching instants in the control strategy.