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Distributed solver for linear matrix inequalities: an optimization perspective
WeijianLi,WenDeng,XianlinZeng,YiguangHong
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(1 Department of Automation, University of Science and Technology of China, Hefei 230027, Anhui, China;2 Key Lab of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;3 Key Laboratory of Intelligent Control and Decision of Complex Systems, School of Automation, Beijing Institute of Technology, Beijing 100081, China;4 Department of Control Science and Engineering, Tongji University, Shanghai 201804, China)
摘要:
In this paper, we develop a distributed solver for a group of strict (non-strict) linear matrix inequalities over a multi-agent network, where each agent only knows one inequality, and all agents co-operate to reach a consensus solution in the intersection of all the feasible regions. The formulation is transformed into a distributed optimization problem by introducing slack variables and consensus constraints. Then, by the primal–dual methods, a distributed algorithm is proposed with the help of projection operators and derivative feedback. Finally, the convergence of the algorithm is analyzed, followed by illustrative simulations.
关键词:  Distributed computation · Distributed optimization · Linear matrix inequalities · Primal–dual method
DOI:https://doi.org/10.1007/s11768-021-00061-z
基金项目:This work was supported by the Shanghai Municipal Science and Technology Major Project (No. 2021SHZDZX0100) and the National Natural Science Foundation of China (Nos. 61733018, 62073035).
Distributed solver for linear matrix inequalities: an optimization perspective
Weijian Li,Wen Deng,Xianlin Zeng,Yiguang Hong
(1 Department of Automation, University of Science and Technology of China, Hefei 230027, Anhui, China;2 Key Lab of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;3 Key Laboratory of Intelligent Control and Decision of Complex Systems, School of Automation, Beijing Institute of Technology, Beijing 100081, China;4 Department of Control Science and Engineering, Tongji University, Shanghai 201804, China)
Abstract:
In this paper, we develop a distributed solver for a group of strict (non-strict) linear matrix inequalities over a multi-agent network, where each agent only knows one inequality, and all agents co-operate to reach a consensus solution in the intersection of all the feasible regions. The formulation is transformed into a distributed optimization problem by introducing slack variables and consensus constraints. Then, by the primal–dual methods, a distributed algorithm is proposed with the help of projection operators and derivative feedback. Finally, the convergence of the algorithm is analyzed, followed by illustrative simulations.
Key words:  Distributed computation · Distributed optimization · Linear matrix inequalities · Primal–dual method