Control of Capacity-Constrained Networks

This thesis concerns control of capacity-constrained networks. These systems involve many agents interconnected by a resource distribution network. The capacity to generate and distribute this resource is constrained. This applies, for instance, to power grids, communication networks, smart surveillance camera networks, and district heating networks. District heating networks in particular are the main focus of this thesis. These systems distribute heat from producers to consumers through hot water pipelines. In this setting, the agents are the consumers in the network, who regulate the flow rate they receive from the network using control valves. Physical limitations limit these flow rates. Therefore, when the demand for heat is high, it may be impossible to satisfy the needs of all the agents. This can result in certain buildings becoming cold. This thesis presents several contributions in this setting.
Firstly: The nature of the flow rate constraints is investigated. In Paper I, it is shown that the set of feasible flow rates in a tree-structured district heating network is convex, allowing for convex optimization-based control structures. One such approach is proposed in the paper, in which the flow rates are distributed fairly between the agents. These control approaches require a model of the system hydraulics. In Paper V, a data-based method for establishing such a model is investigated in a laboratory environment.
Secondly: The limited network capacity should be utilized optimally. This is challenging in the multi-agent setting, where the agents regulate and actuate the flow of resources in a decentralized fashion. Papers II-IV concern controllers which not
only asymptotically guide the network to an optimal resource distribution, but also function in the large-scale, multi-agent setting. These papers show that asymptotic optimality guarantees can be established using variations of standard proportionalintegral control. Papers II and III concern a linear system setting with input saturation, which is extended to a nonlinear setting in Paper IV.