Optimal Energy Consensus Control for Linear Multi-Agent Systems
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- 英文论文题名：Optimal Energy Consensus Control for Linear Multi-Agent Systems
- 论文作者：Han Zhang ; Xiaoming Hu
- 英文论文作者：Han Zhang ; Xiaoming Hu ; Department of Mathematics ; KTH Royal Institute of Technology
- 年：2017
- 作者机构：Department of Mathematics,KTH Royal Institute of Technology;
- 英文论文关键词：Consensus Control ; Multi-Agent Systems ; Optimal Control ; Semi-definite Programming ; Synchronizability
- 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：TP273
- 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：241k
- 原文格式：D
- 会议级别：全国
摘要
In this paper, an optimal energy cost controller for linear multi-agent systems' consensus is proposed. It is assumed that the topology among the agents is fixed and the agents are connected through an edge-weighted graph. The controller only uses relative information between agents. Due to the difficulty of finding the controller gain, we focus on finding the optimal controller among a sub-family whose design is based on Algebraic Riccati Equation(ARE) and guarantee consensus. It is found that the energy cost for such controllers is bounded by an interval and hence we minimize the upper bound. To do that, the control gain and the edge weights are optimized separately. The control gain is optimized by choosing Q = 0 in the ARE; the edge weights are optimized under the assumption that there is limited communication resources in the network. Negative edge weights are allowed, and the problem is formulated as a Semi-definite Programming(SDP) problem. The controller coincides with the optimal control in [8] when the graph is complete. Furthermore, two sufficient conditions for the existence of negative optimal edge weights realization are given.
In this paper, an optimal energy cost controller for linear multi-agent systems' consensus is proposed. It is assumed that the topology among the agents is fixed and the agents are connected through an edge-weighted graph. The controller only uses relative information between agents. Due to the difficulty of finding the controller gain, we focus on finding the optimal controller among a sub-family whose design is based on Algebraic Riccati Equation(ARE) and guarantee consensus. It is found that the energy cost for such controllers is bounded by an interval and hence we minimize the upper bound. To do that, the control gain and the edge weights are optimized separately. The control gain is optimized by choosing Q = 0 in the ARE; the edge weights are optimized under the assumption that there is limited communication resources in the network. Negative edge weights are allowed, and the problem is formulated as a Semi-definite Programming(SDP) problem. The controller coincides with the optimal control in [8] when the graph is complete. Furthermore, two sufficient conditions for the existence of negative optimal edge weights realization are given.
In this paper, an optimal energy cost controller for linear multi-agent systems' consensus is proposed. It is assumed that the topology among the agents is fixed and the agents are connected through an edge-weighted graph. The controller only uses relative information between agents. Due to the difficulty of finding the controller gain, we focus on finding the optimal controller among a sub-family whose design is based on Algebraic Riccati Equation(ARE) and guarantee consensus. It is found that the energy cost for such controllers is bounded by an interval and hence we minimize the upper bound. To do that, the control gain and the edge weights are optimized separately. The control gain is optimized by choosing Q = 0 in the ARE; the edge weights are optimized under the assumption that there is limited communication resources in the network. Negative edge weights are allowed, and the problem is formulated as a Semi-definite Programming(SDP) problem. The controller coincides with the optimal control in [8] when the graph is complete. Furthermore, two sufficient conditions for the existence of negative optimal edge weights realization are given.
引文
[1]F.Borrelli and T.Keviczky,“Distributed lqr design for identical dynamically decoupled systems,”IEEE Transactions on Automatic Control,vol.53,no.8,pp.1901–1912,2008.
[2]Y.Cao and W.Ren,“Optimal linear-consensus algorithms:an lqr perspective,”IEEE Transactions on Systems,Man,and Cybernetics,Part B(Cybernetics),vol.40,no.3,pp.819–830,2010.
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[5]F.G?ring,C.Helmberg,and M.Wappler,“Embedded in the shadow of the separator,”SIAM Journal on Optimization,vol.19,no.1,pp.472–501,2008.
[6]F.Lin,M.Fardad,and M.R.Jovanovic,“Augmented lagrangian approach to design of structured optimal state feedback gains,”IEEE Transactions on Automatic Control,vol.56,no.12,pp.2923–2929,2011.
[7]J.Rogge,J.Suykens,and D.Aeyels,“Consensus over ring networks as a quadratic optimal control problem,”IFAC Proceedings Volumes,vol.43,no.21,pp.317–323,2010.
[8]J.Thunberg and X.Hu,“Optimal output consensus for linear systems:a topology free approach,”Automatica,vol.68,pp.352–356,2016.
[9]H.Trentelman,A.A.Stoorvogel,and M.Hautus,Control theory for linear systems.Springer Science&Business Media,2012.
[10]J.Willems,“Least squares stationary optimal control and the algebraic riccati equation,”IEEE Transactions on Automatic Control,vol.16,no.6,pp.621–634,1971.
[11]H.Zhang and X.Hu,“Consensus control for linear systems with optimal energy cost,”ar Xiv preprint ar Xiv:1612.00316,2016.
[12]H.Zhang,F.L.Lewis,and A.Das,“Optimal design for synchronization of cooperative systems:state feedback,observer and output feedback,”IEEE Transactions on Automatic Control,vol.56,no.8,pp.1948–1952,2011.
[2]Y.Cao and W.Ren,“Optimal linear-consensus algorithms:an lqr perspective,”IEEE Transactions on Systems,Man,and Cybernetics,Part B(Cybernetics),vol.40,no.3,pp.819–830,2010.
[3]P.Deshpande,P.P.Menon,C.Edwards,and I.Postlethwaite,“A distributed control law with guaranteed lqr cost for identical dynamically coupled linear systems,”in Proceedings of the 2011 American Control Conference.IEEE,2011,pp.5342–5347.
[4]J.A.Fax and R.M.Murray,“Information flow and cooperative control of vehicle formations,”IEEE transactions on automatic control,vol.49,no.9,pp.1465–1476,2004.
[5]F.G?ring,C.Helmberg,and M.Wappler,“Embedded in the shadow of the separator,”SIAM Journal on Optimization,vol.19,no.1,pp.472–501,2008.
[6]F.Lin,M.Fardad,and M.R.Jovanovic,“Augmented lagrangian approach to design of structured optimal state feedback gains,”IEEE Transactions on Automatic Control,vol.56,no.12,pp.2923–2929,2011.
[7]J.Rogge,J.Suykens,and D.Aeyels,“Consensus over ring networks as a quadratic optimal control problem,”IFAC Proceedings Volumes,vol.43,no.21,pp.317–323,2010.
[8]J.Thunberg and X.Hu,“Optimal output consensus for linear systems:a topology free approach,”Automatica,vol.68,pp.352–356,2016.
[9]H.Trentelman,A.A.Stoorvogel,and M.Hautus,Control theory for linear systems.Springer Science&Business Media,2012.
[10]J.Willems,“Least squares stationary optimal control and the algebraic riccati equation,”IEEE Transactions on Automatic Control,vol.16,no.6,pp.621–634,1971.
[11]H.Zhang and X.Hu,“Consensus control for linear systems with optimal energy cost,”ar Xiv preprint ar Xiv:1612.00316,2016.
[12]H.Zhang,F.L.Lewis,and A.Das,“Optimal design for synchronization of cooperative systems:state feedback,observer and output feedback,”IEEE Transactions on Automatic Control,vol.56,no.8,pp.1948–1952,2011.