Reaching an Optimal Consensus: Dynamical Systems That Compute Intersections of Convex Sets
Reaching an Optimal Consensus: Dynamical Systems That Compute Intersections of Convex Sets
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达成最佳共识：计算凸集交集的动力系统
DOI：
10.1109/tac.2012.2215261
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发表时间：
2011-12
影响因子：
6.8
通讯作者：
Yiguang Hong
中科院分区：
文献类型：
--
作者：
Guodong Shi;Karl Johansson;Yiguang Hong
在本文中，多代理系统最大程度地限制了一个目标函数的总和，其中每个组件仅是特定节点所知道的，用于与时变互连拓扑的连续时间动力学。假设每个节点都可以观察
In this paper, multi-agent systems minimizing a sum of objective functions, where each component is only known to a particular node, is considered for continuous-time dynamics with time-varying interconnection topologies. Assuming that each node can observe a convex solution set of its optimization component, and the intersection of all such sets is nonempty, the considered optimization problem is converted to an intersection computation problem. By a simple distributed control rule, the considered multi-agent system with continuous-time dynamics achieves not only a consensus, but also an optimal agreement within the optimal solution set of the overall optimization objective. Directed and bidirectional communications are studied, respectively, and connectivity conditions are given to ensure a global optimal consensus. In this way, the corresponding intersection computation problem is solved by the proposed decentralized continuous-time algorithm. We establish several important properties of the distance functions with respect to the global optimal solution set and a class of invariant sets with the help of convex and non-smooth analysis.
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