Continuous-time proportional-integral distributed optimisation for networked systems
Greg N. Droge, Hiroaki Kawashima, Magnus Egerstedt · Journal of Control and Decision · 2014
In this paper, we explore the relationship between dual decomposition and the consensus-based method for distributed optimisation. The relationship is developed by examining the similarities between the two approaches and their relationship to gradient-based constrained optimisation. By formulating each algorithm in continuous-time, it is seen that both approaches use a gradient method for optimisation with one using a proportional control term and the other using an integral control term to drive the system to the constraint set. Therefore, a significant contribution of this paper is to combine these methods to develop a continuous-time proportional-integral distributed optimisation method. Furthermore, we establish convergence using Lyapunov stability techniques and utilising properties from the network structure of the multi-agent system.