Abstract
Unlike the classical distributed consensus protocols that enable a group of agents to reach an agreement regarding a certain quantity of interest in a distributed fashion, the distributed biased min-consensus protocol (DBMC) has been proven to handle the advanced complexity of solving the shortest path problem. Such a protocol is commonly incorporated as the first step of a hierarchical architecture in real applications, such as robot path planning and the management of dispersed computing services. However, a major limitation of DBMC is the lack of results regarding its convergence within a user-assigned time frame. In this article, we first propose two control strategies to ensure that the state error of DBMC decreases exactly to zero or a desired level within a finite time specified by the user. This article further investigates the nominal DBMC itself. By leveraging small-gain-based stability tools and embedding DBMC into a framework applicable to such tools, this article also proves the global exponential input-to-state stability of DBMC, outperforming its current stability results. Simulations are provided to validate the efficacy of our theoretical results.
| Original language | English |
|---|---|
| Pages (from-to) | 8210-8225 |
| Number of pages | 16 |
| Journal | IEEE Transactions on Automatic Control |
| Volume | 70 |
| Issue number | 12 |
| DOIs | |
| Publication status | Published - 2025 |
| MoE publication type | A1 Journal article-refereed |
Funding
This work was supported by the National Science and Technology Major Project of China under Grant No. 2022ZD0120003, the National Natural Science Foundation of China under Grant No. 62303112, Grant No. 62203112 and Grant No. 62233004, and the Natural Science Foundation of Jiangsu Province under Grant No. BK20230826 and Grant No. BK20210216.
Keywords
- Biased min-consensus
- consensus
- pre-specified finite time control
- small-gain theorem
- the shortest path problem
- prespecified finite time (PT) control