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Mathematical Problems in Engineering
Volume 2016, Article ID 6093293, 8 pages
http://dx.doi.org/10.1155/2016/6093293
Research Article

Distributed Function Calculation over Noisy Networks

1College of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan 030600, China
2College of Mechatronics Engineering and Automation, National University of Defense Technology, Changsha 410000, China
3Expedia, Angel Building, St. John Street, London EC1V 4EX, UK
4School of Automation, Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Wuhan 430074, China

Received 21 December 2015; Revised 23 March 2016; Accepted 23 March 2016

Academic Editor: Stefan Balint

Copyright © 2016 Zhidun Zeng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Considering any connected network with unknown initial states for all nodes, the nearest-neighbor rule is utilized for each node to update its own state at every discrete-time step. Distributed function calculation problem is defined for one node to compute some function of the initial values of all the nodes based on its own observations. In this paper, taking into account uncertainties in the network and observations, an algorithm is proposed to compute and explicitly characterize the value of the function in question when the number of successive observations is large enough. While the number of successive observations is not large enough, we provide an approach to obtain the tightest possible bounds on such function by using linear programing optimization techniques. Simulations are provided to demonstrate the theoretical results.