Distributed Minimum Weighted Norm Solution to Linear Equations   Associated with Weighted Inner Product

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	Distributed Minimum Weighted Norm Solution to Linear Equations Associated with Weighted Inner Product
	Wang, Peng ; Ren, Wei ; Duan, Zhisheng
	2016
英文摘要	In this paper, we propose a distributed method to find the solution of the linear equations Ax = b with minimum energy, i.e. the minimum weighted norm associated with the weighted inner product. We first prove that for a special case when the norm is two-norm, the algorithm can make multiple agents reach the minimum two-norm solution of the global linear equations Ax - b if the agents are initialized at the minimum two-norm solutions of their local equations. We then prove that if there are bounded initialization errors, the final convergence of the algorithm is also bounded away from the minimum two-norm solution of the global linear equations. Next, we prove the case with the two-norm replaced with a weighted norm associated with the weighted inner product. Finally, simulation examples are presented to show the effectiveness of the results in this paper.; National Science Foundation [ECCS-1307678]; National Natural Science Foundation of China [61528301]; CPCI-S(ISTP); 5220-5225
会议录	55th IEEE Conference on Decision and Control (CDC)
语种	英语
内容类型	会议论文
源URL	[http://ir.pku.edu.cn/handle/20.500.11897/470244]
专题	工学院
推荐引用方式 GB/T 7714	Wang, Peng,Ren, Wei,Duan, Zhisheng. Distributed Minimum Weighted Norm Solution to Linear Equations Associated with Weighted Inner Product[C]. 见:.