A distributed PID controller for network congestion control problems

This paper describes a (re)design framework of distributed Proportional-Integral-Derivative (PID) control for network congestion control problems at the level of fluid-flow models. Motivated by the augmented Lagrangian method, we introduce extra dynamics to algorithms resulting from traditional primal-dual methods to improve their performance while guaranteeing stability. The modified dynamics contain PID control action, and moreover, the implementation of the scheme remains distributed. We study the influence of the gains resulting from the extra dynamics on system robustness. The performance of the distributed PID controller is illustrated by a numerical example.