Consensus networks over finite fields
Consensus networks over finite fields
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DOI：
10.1016/j.automatica.2013.11.011
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发表时间：
2013-01
期刊：
影响因子：
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通讯作者：
F. Pasqualetti;D. Borra;F. Bullo
中科院分区：
文献类型：
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作者：
F. Pasqualetti;D. Borra;F. Bullo
这项工作研究了有限的内存，计算和通信能力的代理网络的共识策略。我们假设代理只能处理有限字母表中的值，并且我们采用有限域的框架，其中字母表由整数{0，...，p− 1}组成，对于某个素数p，并且操作是以p为模执行的。因此，我们定义了一类新的共识动态，可以在某些应用中利用，例如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值的充分必要条件，以保证收敛。我们证明了有限域上的共识网络在有限时间内收敛，这是在真实的数域上很难实现的一个特征。对于有限域共识网络的设计，我们提出了一个通用的设计方法，具有较高的计算复杂性，和网络的组成规则，从较小的组件生成大的共识网络。最后，我们讨论了有限域一致性网络在传感器网络中的分布平均和姿态估计中的应用。
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.