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arXiv 1301.4587eess.SYcs.SYmath.OC
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有限域上的共识网络

Consensus Networks over Finite Fields

University of California, Santa Barbara(加利福尼亚大学圣塔芭芭拉分校)

Fabio Pasqualetti, Domenica Borra, Francesco Bullo

AI总结:

针对有限内存、计算和通信能力的智能体网络,提出有限域上的共识动力学,给出收敛的充要条件,并设计网络合成方法,应用于分布式平均和姿态估计。

摘要:

本文研究了具有有限内存、计算和通信能力的智能体网络的共识策略。我们假设智能体只能处理来自有限字母表的值,并采用有限域框架,其中字母表由整数{0,...,p-1}组成(p为素数),运算在模p下进行。因此,我们定义了一类新的共识动力学,可在某些应用中利用,例如在容量和内存受限的传感器网络中的姿态估计。对于有限域上的共识网络,我们给出了网络拓扑和权重确保收敛的充分必要条件。我们证明有限域上的共识网络在有限时间内收敛,这一特性在实数域上很难实现。对于有限域共识网络的设计,我们提出了一种具有高计算复杂度的通用设计方法,以及一种从较小组件生成大型共识网络的网络组合规则。最后,我们讨论了有限域共识网络在传感器网络中的分布式平均和姿态估计中的应用。

英文摘要:

This work studies consensus strategies for networks of agents with limited memory, computation, and communication capabilities. We assume that agents can process only values from a finite alphabet, and we adopt the framework of finite fields, where the alphabet consists of the integers {0,...,p-1}, for some prime number p, and operations are performed modulo p. Thus, we define a new class of consensus dynamics, which can be exploited in certain applications such as pose estimation in capacity and memory constrained sensor networks. For consensus networks over finite fields, we provide necessary and sufficient conditions on the network topology and weights to ensure convergence. We show that consensus networks over finite fields converge in finite time, a feature that can be hardly achieved over the field of real numbers. For the design of finite-field consensus networks, we propose a general design method, with high computational complexity, and a network composition rule to generate large consensus networks from smaller components. Finally, we discuss the application of finite-field consensus networks to distributed averaging and pose estimation in sensor networks.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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