Hybrid protocols for leader–follower consensus of multi-agent systems with distributed delays
Bibliographic record
Abstract
The primary focus of this paper is to investigate the leader–follower consensus problem of multi-agent systems (MASs) with discrete and distributed delays in complex domains. We propose a new hybrid consensus protocol that incorporates a continuous-time protocol based on the communication topology of follower agents, along with an event-triggered pinning impulsive control (ETPIC) protocol. Using the Lyapunov functional method in complex domains, we establish delay-dependent sufficient conditions for leader–follower consensus of delayed complex-valued MASs. Our results demonstrate that the proposed hybrid protocol can ensure leader–follower consensus even when the size of discrete and distributed delays exceeds the length of intervals between two consecutive triggering instants. Furthermore, we prove that the Zeno phenomenon can be excluded under the proposed control protocol. In particular, as a special case, we derive the leader–follower consensus result for delay-free complex-valued MASs based on a reduced hybrid control protocol. Two numerical examples are presented to validate the effectiveness of the proposed control scheme.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".