An Asynchronous Distributed Algorithm for Solving a Linear Algebraic Equation

被引:0
作者
Liu, Ji [1 ]
Mou, Shaoshuai [2 ]
Morse, A. Stephen [2 ]
机构
[1] Univ Illinois, Coordinated Sci Lab, Urbana, IL 61801 USA
[2] Yale Univ, New Haven, CT 06520 USA
来源
2013 IEEE 52ND ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC) | 2013年
关键词
CONSTRAINED CONSENSUS; RECONSTRUCTION;
D O I
暂无
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
A distributed algorithm is described for solving a linear algebraic equation of the form Ax = b where A is a matrix for which the equation has at least one solution. The equation is simultaneously and asynchronously solved by m agents assuming each agent knows only a subset of the rows of the partitioned matrix [A b], the estimates of the equation's solution generated by its neighbors, and nothing more. Each agent recursively updates its estimate of a solution at its own event times by utilizing estimates generated by each of its neighbors which are transmitted with delays. Each agent has its own event time sequence and the event time sequences of different agents are not assumed to be synchronized. Neighbor relations are characterized by a time-dependent directed graph whose vertices correspond to agents and whose arcs depict neighbor relations. It is shown that for any matrix A for which the equation has a solution and any repeatedly jointly strongly connected sequence of neighbor graphs defined on the merged sequence of all agents' event times, the algorithm causes all agents' estimates to converge exponentially fast to the same solution to Ax = b
引用
收藏
页码:5409 / 5414
页数:6
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