摘要
In this paper,we explore the relationship between dual decomposition and the consensusbased 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.
基金
The work by M.Egerstedt was funded by The Air Force Office of Scientific Research through[grant number 2012-00305-01].
作者简介
Corresponding author:Greg Droge,received the BS degree in Electrical Engineering from Brigham Young University,Provo,Utah.He received his MS and PhD from the school of Electrical and Computer Engineering at the Georgia Institute of Technology in 2012 and 2014,respectively.His research interests include model predictive control and distributed optimisation with emphasis in motion planning and control,Email:gregdroge@gatech.edu;Hiroaki Kawashima,received his MS and PhD in informatics from Kyoto University,Japan in 2001 and 2007,respectively.He is currently a senior lecturer at the Graduate School of Informatics,Kyoto University,Japan.From 2010 to 2012,he was a JSPS postdoctoral fellow for Research Abroad,and a visiting researcher at the School of Electrical and Computer Engineering,Georgia Institute of Technology.His research interests include hybrid systems,networked control systems,pattern recognition,machine learning,and human-computer interaction.He is a member of the IEEE;Magnus B.Egerstedt,(S’99-M’00-SM’05-F’12)is a professor in the School of Electrical and Computer Engineering at the Georgia Institute of Technology.He received the MS degree in Engineering Physics and the PhD degree in Applied Mathematics from the Royal Institute of Technology,Stockholm,Sweden,in 1996 and 2000,respectively,and he received BA degree in Philosophy from Stockholm University in 1996.His research interests include hybrid and networked control,with applications in motion planning,control,and coordination of mobile robots,and he is the director of the Georgia Robotics and Intelligent Systems Laboratory(GRITS Lab),is a fellow of the IEEE,and received the CAREER Award from the US National Science Foundation in 2003.
