Anti-windup coordination strategy around a fair equilibrium in resource sharing networks

We coordinate interconnected agents where the control input of each
agent is limited by the control input of others. In that sense, the sys-
tems have to share a limited resource over a network. Such problems can
arise in different areas and it is here motivated by a district heating ex-
ample. When the shared resource is insufficient for the combined need
of all systems, the resource will have to be shared in an optimal fash-
ion. In this scenario, we want the systems to automatically converge to
an optimal equilibrium. The contribution of this paper is the proposal
of a control architecture where each separate system is controlled by a
local PI controller. The controllers are then coordinated through a global
rank-one anti-windup signal. It is shown that the equilibrium of the pro-
posed closed-loop system minimizes the infinity-norm of stationary state
deviations. A proof of linear-domain passivity is given, and a numerical
example highlights the benefits of the proposed method with respect to
the state-of-the-art.