Model-free Output Consensus Control for Heterogeneous Nonlinear Multi-agent Systems
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摘要: 针对异构非线性多智能体系统的输出一致性控制难题, 设计了一种基于同胚分布式控制协议的无模型方法. 通过将输出反馈线性化理论与自适应动态规划相结合, 可以在不需要精确系统模型的情况下实现非线性智能体的线性化, 简化分布式控制器的设计复杂性. 具体而言, 通过设计双层分布式控制结构, 在物理空间层通过无模型反馈线性书方法实现未知系统线性化, 在微分同构空间层利用线性控制方法进行分布式共识控制. 通过两个实验验证了所提方法在处理未知异构非线性多智能体系统中的有效性, 将传统的线性分布式控制方法扩展到未知非线性多智能体控制器设计问题.Abstract: A model-free method based on homeomorphic distributed control protocol is proposed to address the output consensus control problem of heterogeneous nonlinear multi-agent systems. By integrating output feedback linearization theory with adaptive dynamic programming, this approach linearizes nonlinear agents without requiring precise system models, simplifying the design of distributed controllers. Specifically, a two-layer distributed control structure is designed: in the physical space layer, model-free feedback linearization is applied to linearize unknown systems, while in the diffeomorphic space layer, linear control techniques are used for distributed consensus control. The effectiveness of the proposed method in handling unknown heterogeneous nonlinear multi-agent systems is validated through two experiments, extending traditional linear distributed control methods to the design of controllers for unknown nonlinear multi-agent systems.
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图 1 同胚分布式控制协议结构图
Fig. 1 Structure diagram of homeomorphic distributed control protocol
图 4 学习前后输出和一致性误差轨迹对比((a)初始一致性误差轨迹; (b)学习收敛后一致性误差轨迹; (c)初始输出轨迹; (d)学习收敛后输出轨迹)
Fig. 4 The output and output error trajectory comparison before and after learning ((a) initial consensus error trajectory; (b) the consensus error trajectory after learning convergence; (c) initial output trajectory; (d) output trajectory after learning convergence))
图 7 网络更新损失演化轨迹((a)评价网络更新损失; (b)奖励网络更新损失)
Fig. 7 Evolution trajectory of network update loss ((a) Critic network update loss; (b) Reward network update loss)
图 8 学习收敛后输出一致性轨迹切换实验
Fig. 8 Output consensus trajectory switching experiment after learning convergence
表 1 异构多智能体系统参数
Table 1 Heterogeneous multi-agent system parameters
变量 值 (m) 变量 值 (m) 变量 值 (m) $ {m_1} $ 0.04 $ {m_2} $ 0.04 $ {m_3} $ 0.06 $ {h_1} $ 0.06 $ {h_2} $ 0.04 $ {h_3} $ 0.06 $ {m_4} $ 0.06 $ {m_5} $ 0.08 $ {m_6} $ 0.08 $ {h_4} $ 0.04 $ {h_5} $ 0.06 $ {h_6} $ 0.04 
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表 2 学习参数设置
Table 2 Learning parameter
参数 值 参数 值 参数 值 $ {\eta _r} $ 0.05 $ {\eta _c} $ 0.02 $ {\eta _a} $ 0.01 $ \gamma $ 0.9 $ {\mu _j} $ 0.01 $ {\mu _\lambda } $ 0.01 $ \varepsilon_i $ 0.08 $ H $ $ [1,\; 0.2] $
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