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Consensus for Second-Order Discrete-Time Agents With Position Constraints and Delays.

Peng Lin, Yali Liao, Hairong Dong

    IEEE Transactions on Cybernetics
    |April 19, 2021
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    Summary

    This study presents a distributed algorithm for second-order discrete-time agents to achieve consensus in networks with constraints and delays. Agents converge to a common point while respecting their position limits, even with switching topologies and communication delays.

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    Area of Science:

    • Control Systems Engineering
    • Networked Systems
    • Distributed Computing

    Background:

    • Consensus problems are crucial for coordinating multi-agent systems.
    • Challenges include discrete-time dynamics, network constraints, and communication imperfections.
    • Existing methods often struggle with nonuniform constraints and switching topologies.

    Purpose of the Study:

    • To develop a distributed consensus algorithm for second-order discrete-time agents.
    • To address nonuniform position constraints and switching network topologies.
    • To incorporate communication delays into the consensus analysis.

    Main Methods:

    • A projection operation ensures agents remain within specified convex sets.
    • A distributed algorithm is designed for consensus achievement.
    • Linear transformation converts the system for analysis, merging nonlinear terms.
    • Non-negative matrix properties are used to prove convergence.

    Main Results:

    • The proposed algorithm guarantees consensus convergence for all agents.
    • Agents maintain their positions within individual constraint sets.
    • Convergence is achieved despite communication delays and switching topologies.
    • The union of communication graphs over time intervals must be strongly connected.

    Conclusions:

    • The developed distributed algorithm effectively solves the consensus problem for second-order discrete-time agents under complex network conditions.
    • The method ensures agents reach agreement while respecting individual constraints, demonstrating robustness to delays and topology changes.
    • Numerical simulations validate the theoretical findings, confirming the algorithm's practical applicability.