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Optimal consensus control for unknown second-order multi-agent systems: Using model-free reinforcement learning method

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  • Li, Jun
  • Ji, Lianghao
  • Li, Huaqing

Abstract

In this paper, the optimal consensus control problem with second-order dynamics consisting of leader and follower agents is discussed. For optimal consensus problem, the optimal control policies rely on algebraic Riccati equations (AREs) equation, which are difficult to solve. Furthermore, both the follower agents’ and the leader agent’s dynamics are assumed to be completely unknown. As the consensus problem based on feedback control, the second-order discrete-time multi-agent systems (DT-MASs) model with directed topology is formulated to the optimal tracking control problem via online deep reinforcement learning method. Based on graph theory, matrix analysis, Lyapunov stability, deep learning and optimal control, the optimality of value function and the stability of the consensus error systems for the unknown second-order systems are guaranteed for each agent. The results show that the designed policy iteration algorithm not only stabilizes the distributed dynamic systems, but also makes all agents’ position and velocity states reach consensus, respectively. Finally, the correctness of our theoretical results is illustrated under two numerical simulations based on the designing model-free actor-critic networks.

Suggested Citation

  • Li, Jun & Ji, Lianghao & Li, Huaqing, 2021. "Optimal consensus control for unknown second-order multi-agent systems: Using model-free reinforcement learning method," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    • Handle: RePEc:eee:apmaco:v:410:y:2021:i:c:s0096300321005403
    DOI: 10.1016/j.amc.2021.126451
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    References listed on IDEAS

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    1. Yilun Shang, 2015. "Group consensus of multi-agent systems in directed networks with noises and time delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(14), pages 2481-2492, October.
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    Cited by:

    1. Wang, Yun & Fang, Tian & Kong, Qingkai & Li, Feng, 2024. "Zero-sum game-based optimal control for discrete-time Markov jump systems: A parallel off-policy Q-learning method," Applied Mathematics and Computation, Elsevier, vol. 467(C).
    2. Xu, Jiahong & Wang, Lijie & Liu, Yang & Sun, Jize & Pan, Yingnan, 2022. "Finite-time adaptive optimal consensus control for multi-agent systems subject to time-varying output constraints," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    3. Li, Jingwang & An, Qing & Su, Housheng, 2023. "Proximal nested primal-dual gradient algorithms for distributed constraint-coupled composite optimization," Applied Mathematics and Computation, Elsevier, vol. 444(C).
    4. Liu, Xinrui & Zhang, Mingchao & Xie, Xiangpeng & Zhao, Liang & Sun, Qiuye, 2022. "Consensus-based energy management of multi-microgrid: An improved SoC-based power coordinated control method," Applied Mathematics and Computation, Elsevier, vol. 425(C).

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