Aspects of Fairness in Robust, Distributed Control of Interconnected Systems

This paper studies the distribution of parameter values in large-scale interconnected systems. Using γ-robustness, a bound on the effect of external disturbances acting on subsystems can be found. However, due to the interconnected nature of the system, the same bound can be reached with different choices of distributed control parameters leading to different local control costs. A notion of fairness and a measurement of unfairness is presented to describe and measure the effects of unevenly distributed parameters in the system. The distribution of bounds on state deviations due to external disturbances is studied and conditions and algorithms are given to ensure such bounds while fairly distributing the required control efforts. Decentralized algorithms to reach fairness or reduce unfairness are presented for various assumptions on systems and constraints. The results are illustrated by examples.