Decentralized PI-control and Anti-windup in Resource Sharing Networks

We consider control of multiple stable first-order \review{agents} which have a control coupling described by an M-matrix. These agents are subject to incremental sector-bounded \review{input} nonlinearities. We show that such plants can be globally asymptotically stabilized to a unique equilibrium using fully decentralized proportional-integral controllers equipped with anti-windup and subject to local tuning rules. In addition, we show that when the nonlinearities correspond to the saturation function, the closed loop asymptotically minimizes a weighted 1-norm of the agents state mismatch. The control strategy is finally compared to other state-of-the-art controllers on a numerical district heating example.