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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) |
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| 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 |
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| 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). |
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| 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 |
