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<p>The aim of this study is to investigate the optimal consensus problem for discrete-time multi-agent systems with input constraints by data-based reinforcement learning algorithms. Creating a protocol that will enable all followers to reach consensus with the leader while minimizing the performance index is the task of the optimum consensus problem. Generally, the solution of this problem relies on the coupled Hamilton-Jacobi-Bellman equation. Nevertheless, it is challenging to explicitly derive the analytical solution for the Hamilton-Jacobi-Bellman equation. Furthermore, it is hard to find precise mathematical representations of the majority of real-world systems. In this study, addressing these challenges, we utilize actor-critic neural networks to implement the algorithm, relying on system data rather than system models. To address the input constraints, the projection operator and the Frank-Wolfe methods are introduced. Then, we design the projection reinforcement learning algorithm and the projection-free reinforcement learning algorithm, the convergence and stability are examined. Integrating further the benefits of two algorithms, an comprehensive algorithm is introduced. Finally, the algorithms are validated through numerical examples, demonstrating their efficacy.</p>

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Data-based Optimal Consensus of Multi-agent Systems With Reinforcement Learning Algorithms

  • 期刊论文

  • 发表日期：

    2025年5月14日

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  • Lipo Mo,
  • Ruoxun Ma,
  • Min Zuo,
  • Ke Guo

摘要

The aim of this study is to investigate the optimal consensus problem for discrete-time multi-agent systems with input constraints by data-based reinforcement learning algorithms. Creating a protocol that will enable all followers to reach consensus with the leader while minimizing the performance index is the task of the optimum consensus problem. Generally, the solution of this problem relies on the coupled Hamilton-Jacobi-Bellman equation. Nevertheless, it is challenging to explicitly derive the analytical solution for the Hamilton-Jacobi-Bellman equation. Furthermore, it is hard to find precise mathematical representations of the majority of real-world systems. In this study, addressing these challenges, we utilize actor-critic neural networks to implement the algorithm, relying on system data rather than system models. To address the input constraints, the projection operator and the Frank-Wolfe methods are introduced. Then, we design the projection reinforcement learning algorithm and the projection-free reinforcement learning algorithm, the convergence and stability are examined. Integrating further the benefits of two algorithms, an comprehensive algorithm is introduced. Finally, the algorithms are validated through numerical examples, demonstrating their efficacy.