On the design and control of compartmental networks for optimal evacuation and supply (2017)
An optimization problem that minimizes the stable scaled consensus state for linear compartmental systems is proposed. The minimum scaled consensus state (MSCS) methodology is used to solve the optimal evacuation and supply problems under operational constraints. The problem can be solved off-line under static disturbances, and on-line for time-varying disturbances. It is shown for the static case that the MSCS problem is equivalent to the digraph balancing problem. When the proposed optimization problem is solved on-line, the resultant MSCS controller is of feedforward nature and a solution can be found efficiently for large-scale systems, since the optimization problem underlying the MSCS control is linear for the optimal evacuation problem, and convex for the optimal supply problem. Moreover, a mixed-integer programming problem is proposed to determine the minimum number of actuators required to achieve the MSCS when there are budget constraints to upgrade an existing compartmental network. Several case studies in the context of water drainage and water distribution systems are presented to show the effectiveness of the proposed methodologies.