Singularly Perturbed Dynamics for Distributed Multi-agent Optimization
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- 英文论文题名：Singularly Perturbed Dynamics for Distributed Multi-agent Optimization
- 论文作者：Maojiao Ye ; Guoqiang Hu
- 英文论文作者：Maojiao Ye ; Guoqiang Hu ; School of Electrical and Electronic Engineering ; Nanyang Technological University
- 年：2017
- 作者机构：School of Electrical and Electronic Engineering,Nanyang Technological University;
- 英文论文关键词：Distributed optimization ; leader-following consensus ; strongly connected graph
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（B）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（B）
- 语种：英文
- 分类号：TP18
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：6
- 文件大小：574k
- 原文格式：D
- 会议级别：全国
摘要
Distributed algorithms are proposed to solve distributed optimization problems for a network of strongly connected agents in this paper. The proposed algorithms are based on a combination of a leader-following consensus protocol and the gradient descent method/primal-dual dynamics. In the leader-following consensus protocol, each agent acts as a virtual leader that provides its local measurements(i.e., local decision variables and gradient information) as reference signals to be followed by all the agents in the network. Based on the estimated information, the gradient methods are implemented. By utilizing the proposed methods, each agent produces an estimation on the minimization solution to the distributed optimization problem.Unconstrained distributed optimization problems are firstly addressed followed by distributed optimization problems with a balance constraint. Analytical convergence analysis is provided for both scenarios.
Distributed algorithms are proposed to solve distributed optimization problems for a network of strongly connected agents in this paper. The proposed algorithms are based on a combination of a leader-following consensus protocol and the gradient descent method/primal-dual dynamics. In the leader-following consensus protocol, each agent acts as a virtual leader that provides its local measurements(i.e., local decision variables and gradient information) as reference signals to be followed by all the agents in the network. Based on the estimated information, the gradient methods are implemented. By utilizing the proposed methods, each agent produces an estimation on the minimization solution to the distributed optimization problem.Unconstrained distributed optimization problems are firstly addressed followed by distributed optimization problems with a balance constraint. Analytical convergence analysis is provided for both scenarios.
Distributed algorithms are proposed to solve distributed optimization problems for a network of strongly connected agents in this paper. The proposed algorithms are based on a combination of a leader-following consensus protocol and the gradient descent method/primal-dual dynamics. In the leader-following consensus protocol, each agent acts as a virtual leader that provides its local measurements(i.e., local decision variables and gradient information) as reference signals to be followed by all the agents in the network. Based on the estimated information, the gradient methods are implemented. By utilizing the proposed methods, each agent produces an estimation on the minimization solution to the distributed optimization problem.Unconstrained distributed optimization problems are firstly addressed followed by distributed optimization problems with a balance constraint. Analytical convergence analysis is provided for both scenarios.
引文
[1]A.Nedic,S.Lee and M.Raginsky,“Decentralized online optimizatgion with global objectives and local communication,”American Control Conference,pp.4497-4503,2015.
[2]S.Liu,L.Xie and C.Liu,“Consensus based constrained optimization for multi-agent systems,”IEEE Conference on Decision and Control,pp.5450-5455,2015.
[3]Z.Jiang,S.Sarkar and K.Mukherjee,“On distributed optimization using generalized gossip,”IEEE Conference on Decision and Control,pp.2667-2672,2015.
[4]A.Nedic and A.Olshevsky,“Distributed optimization over time-varying directed graphs,”IEEE Transactions on Automatic Control,vol.60,pp.601-615,2015.
[5]S.Boyd,N.Parikh,E.Chu,B.Peleato and J.Eckstein,“Distributed optimization and statistical learning via the alternating direction method of multiplier,”Foundations and Trends in Machine Learning,vol.3,pp.1-122,2011.
[6]P.Lin,W.Ren and Y.Song,“Distributed multi-agent optimization subject to nonidentical constraints and communication delays,”Automatica,vol.65,pp.120-131,2016.
[7]G.Droge,H.Kawashima and M.Egerstedt,“Continuoustime proportional-integral distributed optimization for networked systems,”Journal of Decision and Control,vol.1,pp.191-213,2014.
[8]M.Ye and G.Hu,“Distributed extremum seeking for constrained networked optimization and its application to energy consumption control in smart grid,”IEEE Transactions on Control Systems Technology,vol.24,pp.2048-2058,2016.
[9]S.Kia,J.Cortes and S.Martinez,“Distributed convex optimization via continuous-time coordination algorithmns with discrete-time communication,”Automatica,vol.55,pp.254-264,2015.
[10]N.Li and J.Marden,“Designing games for distributed optimization,”IEEE Journal of Selected Topics in Signal Processing,vol.7,pp.230-242,2013.
[11]J.Wang and N.Elia,“Control approach to distributed optimization,”Allerton Conference on Communications,Control and Computing,pp.557-561,2010.
[12]J.Wang and N.Elia,“A control perspective for centralized and distributed convex optimization,”IEEE Conference on Decision and Control,pp.3800-3805,2011.
[13]M.Ye and G.Hu,“Distributed optimization for systems with time-varying quadratic objective functions,”IEEE Conference on Decision and Control,pp.3285-3290,2015.
[14]B.Gharesifard and J.Cortes,“Distributed continuous-time convex optimization on weight-balanced digraphs,”IEEETransactions on Automatic Control,vol.59,pp.781-786,2014.
[15]A.Menon and J.Baras,“Collaborative extremum seeking for welfare optimization,”IEEE Conference on Decision and Control,pp.346-351,2014.
[16]S.Dougherty and M.Guay,“Extremum-seeking control of distributed systems using consensus estimation,”IEEE Conference on Decision and Control,pp.3450-3455,2014.
[17]L.Bai,M.Ye,C.Sun and G.Hu,“Distributed control for optimal economic dispatch via saddle point dynamics and consensus algorithms,”IEEE Conference on Decision and Control,pp.6934-6939,2016.
[18]M.Ye and G.Hu,“Game design and analysis for price based demand response:an aggregate game approach”,IEEETransactions on Cybernetics,vol.47,no.3,pp.720-730,2017.
[19]M.Ye and G.Hu,“Distributed Nash equilibrium seeking by a consensus based approach,”IEEE Transactions on Automatic Control,accepted,to appear,DOI:10.1109/TAC.2017.2688452.
[20]M.Ye and G.Hu,“Simultaneous social cost minimization and Nash equilibrium seeking in non-cooperative games,”Chinese Control Conference,2017,accepted,to appear.
[21]F.Lewis,H.Zhang and K.Hengster-Movric and A.Das,Cooperative Control of Multi-agent Systems:Optimal and Adaptive Design Approach,Springer-Verlag,2014.
[22]H.Khailil,Nonlinear System,Prentice Hall,3rd edtion,2002.
[23]D.Bertsekas,A.Nedic and A.Ozdaglar,Convex analysis and optimization,Athena Scientific,2003.
[24]S.Boyd and L.Vandenberghe,Convex Optimization,Cambridge University Press,2009.
1 The notations ,IN×Nare defined in Section 2.
2 Note that this is only for notational convenience and the proposed method can be directly adapted to address x∈RM,where M is a positive integer.
[2]S.Liu,L.Xie and C.Liu,“Consensus based constrained optimization for multi-agent systems,”IEEE Conference on Decision and Control,pp.5450-5455,2015.
[3]Z.Jiang,S.Sarkar and K.Mukherjee,“On distributed optimization using generalized gossip,”IEEE Conference on Decision and Control,pp.2667-2672,2015.
[4]A.Nedic and A.Olshevsky,“Distributed optimization over time-varying directed graphs,”IEEE Transactions on Automatic Control,vol.60,pp.601-615,2015.
[5]S.Boyd,N.Parikh,E.Chu,B.Peleato and J.Eckstein,“Distributed optimization and statistical learning via the alternating direction method of multiplier,”Foundations and Trends in Machine Learning,vol.3,pp.1-122,2011.
[6]P.Lin,W.Ren and Y.Song,“Distributed multi-agent optimization subject to nonidentical constraints and communication delays,”Automatica,vol.65,pp.120-131,2016.
[7]G.Droge,H.Kawashima and M.Egerstedt,“Continuoustime proportional-integral distributed optimization for networked systems,”Journal of Decision and Control,vol.1,pp.191-213,2014.
[8]M.Ye and G.Hu,“Distributed extremum seeking for constrained networked optimization and its application to energy consumption control in smart grid,”IEEE Transactions on Control Systems Technology,vol.24,pp.2048-2058,2016.
[9]S.Kia,J.Cortes and S.Martinez,“Distributed convex optimization via continuous-time coordination algorithmns with discrete-time communication,”Automatica,vol.55,pp.254-264,2015.
[10]N.Li and J.Marden,“Designing games for distributed optimization,”IEEE Journal of Selected Topics in Signal Processing,vol.7,pp.230-242,2013.
[11]J.Wang and N.Elia,“Control approach to distributed optimization,”Allerton Conference on Communications,Control and Computing,pp.557-561,2010.
[12]J.Wang and N.Elia,“A control perspective for centralized and distributed convex optimization,”IEEE Conference on Decision and Control,pp.3800-3805,2011.
[13]M.Ye and G.Hu,“Distributed optimization for systems with time-varying quadratic objective functions,”IEEE Conference on Decision and Control,pp.3285-3290,2015.
[14]B.Gharesifard and J.Cortes,“Distributed continuous-time convex optimization on weight-balanced digraphs,”IEEETransactions on Automatic Control,vol.59,pp.781-786,2014.
[15]A.Menon and J.Baras,“Collaborative extremum seeking for welfare optimization,”IEEE Conference on Decision and Control,pp.346-351,2014.
[16]S.Dougherty and M.Guay,“Extremum-seeking control of distributed systems using consensus estimation,”IEEE Conference on Decision and Control,pp.3450-3455,2014.
[17]L.Bai,M.Ye,C.Sun and G.Hu,“Distributed control for optimal economic dispatch via saddle point dynamics and consensus algorithms,”IEEE Conference on Decision and Control,pp.6934-6939,2016.
[18]M.Ye and G.Hu,“Game design and analysis for price based demand response:an aggregate game approach”,IEEETransactions on Cybernetics,vol.47,no.3,pp.720-730,2017.
[19]M.Ye and G.Hu,“Distributed Nash equilibrium seeking by a consensus based approach,”IEEE Transactions on Automatic Control,accepted,to appear,DOI:10.1109/TAC.2017.2688452.
[20]M.Ye and G.Hu,“Simultaneous social cost minimization and Nash equilibrium seeking in non-cooperative games,”Chinese Control Conference,2017,accepted,to appear.
[21]F.Lewis,H.Zhang and K.Hengster-Movric and A.Das,Cooperative Control of Multi-agent Systems:Optimal and Adaptive Design Approach,Springer-Verlag,2014.
[22]H.Khailil,Nonlinear System,Prentice Hall,3rd edtion,2002.
[23]D.Bertsekas,A.Nedic and A.Ozdaglar,Convex analysis and optimization,Athena Scientific,2003.
[24]S.Boyd and L.Vandenberghe,Convex Optimization,Cambridge University Press,2009.
1 The notations ,IN×Nare defined in Section 2.
2 Note that this is only for notational convenience and the proposed method can be directly adapted to address x∈RM,where M is a positive integer.