Weighted Average Consensus-Based Optimization of Advection-Diffusion Systems

You are here

Top Reasons to Join SPS Today!

1. IEEE Signal Processing Magazine
2. Signal Processing Digital Library*
3. Inside Signal Processing Newsletter
4. SPS Resource Center
5. Career advancement & recognition
6. Discounts on conferences and publications
7. Professional networking
8. Communities for students, young professionals, and women
9. Volunteer opportunities
10. Coming soon! PDH/CEU credits
Click here to learn more.

Weighted Average Consensus-Based Optimization of Advection-Diffusion Systems

Saber Jafarizadeh

As a fundamental algorithm for collaborative processing over multi-agent systems, distributed consensus algorithm has been studied for optimizing its convergence rate. Due to the close analogy between the diffusion problem and the consensus algorithm, the previous trend in the literature is to transform the diffusion system from the spatially continuous domain into the spatially discrete one. In this transformation, the optimality is not necessarily preserved. In this paper, the reverse of this approach has been adopted, and it has been shown that the optimality can be preserved. This paper studies optimization of the Continuous-Time Consensus (CTC) problem on a weighted digraph with given average weight. Based on the detailed balance property, the CTC algorithm is converted into the weighted-average CTC algorithm. For the given distribution and average weight, a possible solution procedure has been provided. For finding the optimal weights corresponding to the weighted-average CTC algorithm with optimal convergence rate on a general graph. This solution procedure has been implemented based on the min-max theorem. For path topology, it is shown that the linearity of the drift term is the necessary and sufficient condition for the optimality of the consensus algorithm (and the corresponding diffusion system). Thus, the Pearson's class of discrete (continuous) distributions are optimal, where the closed-form formulas for the convergence rate, spectrum and other characteristics of the corresponding optimal consensus algorithm (diffusion system), i.e., the Hypergeometric types have been provided.

SPS on Twitter

  • On 15 September 2022, we are excited to partner with and to bring you a webinar and roundtable,… https://t.co/we14OUl2QV
  • The SPS Webinar Series continues on Monday, 22 August when Dr. Yu-Huan Wu and Dr. Shanghua Gao present “Towards Des… https://t.co/ZkHjQLLn7L
  • CALL FOR PAPERS: The IEEE/ACM Transactions on Audio, Speech, and Language Processing is now accepting submissions f… https://t.co/wkoVBKfE5j
  • DEADLINE EXTENDED: The IEEE Journal of Selected Topics in Signal Processing is now accepting submissions for a Spec… https://t.co/qoRbzFeMLL
  • Our Information Forensics and Security Webinar Series continues on Tuesday, 23 August when Dr. Anderson Rocha prese… https://t.co/q48hnIMfan

SPS Videos

Signal Processing in Home Assistants


Multimedia Forensics

Careers in Signal Processing             


Under the Radar