Optimality Loss Minimization in Distributed Control with Application to District Heating

This paper presents a novel partitioning method designed to minimize control performance degradation resulting from partitioning a system for distributed control while maintaining the computational benefits of these methods. A game-theoretic performance metric, the modified Price of Anarchy, is introduced and is used in a generalizable partitioning metric to quantify optimality losses in a distributed controller. By finding the partition that minimizes the partitioning metric, the best-performing distributed control design is chosen. The presented partitioning metric is control-design agnostic, making it broadly applicable to many control design problems. In this paper, the developed metric is used to minimize the performance losses in the distributed control of a demand-flexible District Heating Network. The final distributed controller is provably feasible and stable. In simulation, this novel partitioning performed similarly to the centralized controller, increasing overall heat losses by only 1.9%, as compared to a similarly-sized baseline partition, which resulted in a 22% increase in losses.