Continuous-Time Biased Min-Consensus

  • Yinyan Zhang
  • Shuai Li


In this chapter, we present an interesting result of a modified min-consensus protocol, which is referred to as the biased min-consensus for continuous-time multi-agent systems. Through a proper modification, we show that the modified protocol can generate a totally different behavior of the agents in the multi-agent system. Specifically, with the min-consensus protocol, the state values of the all agents in the multi-agent system globally asymptotically converge to the minimum of the initial state values. However, when the biased min-consensus protocol is adopted, the agents states are still globally asymptotically convergent but the state values of the agents in the multi-agent system are not necessarily the same, which essentially can constitute a solution to the shortest path problem defined in the graph according to our theoretical analysis on the biased min-consensus protocol. This shows that by modifying an existing consensus protocol, we may have higher-level intelligence for the simple agents, leading to the new perspective about whether intelligence can be generated via the usage of control theory. To evaluate the performance of the biased min-consensus protocol and validate the theoretical results, we perform simulations about the shortest path finding over both simple graphs with only a few nodes and complicated graphs with more than 40,000 nodes. A direct extension of the presented method to the complete coverage problem of mobile robots further demonstrate the potential of the presented result in the practice.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Yinyan Zhang
    • 1
  • Shuai Li
    • 2
  1. 1.College of Cyber SecurityJinan UniversityGuangzhouChina
  2. 2.School of EngineeringSwansea UniversitySwanseaUK

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