鲁棒博弈动力学: 分析与综合
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TP13

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国家自然科学基金项目(62036002).


Robust game dynamics: Analysis and synthesis
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    摘要:

    不确定性广泛存在于各种自然和工程系统中, 这对系统动力学的建模、分析、预测和控制提出巨大挑战. 对于工程控制系统, 已经发展出鲁棒控制相关理论以研究不确定性对系统动力学的影响及其综合设计问题. 然而, 对于大规模人在环路的集群自主系统, 不确定性下的系统动力学研究仍处于起步阶段. 鉴于此, 将经典控制系统中鲁棒控制的概念和方法扩展到大规模集群自主系统, 提出鲁棒博弈动力学的分析和综合方法, 针对类典型的不确定性研究了系统的演化动力学, 并结合经济学、心理学、社会学中的期望效用理论探讨博弈群体对不确定性的主观响应. 不确定性可以逆转经典博弈动力学的演化方向以及产生多稳态和周期振荡极限环等丰富的动力学行为, 所作研究揭示了不确定性对集群自主系统演化的重要影响以及群体博弈系统动力学的复杂性.

    Abstract:

    Uncertainty exists in a wide range of natural and engineering systems, posing great challenges to the modeling, analysis, prediction and control of system dynamics. For engineering control systems, robust control theory has been developed to study the effect of uncertainty on system dynamics and its resistance to disturbance. However, the study of system dynamics under uncertainty in large-scale autonomous systems with humans in the loop is still in its infancy. In this paper, the concept of robust dynamics is extended to large-scale collective systems, and a robust game dynamics analysis method is proposed. Based on the proposed framework, three typical types of uncertainty are studied, and the subjective response of agents to uncertainty is also explored by combining the expected utility theory in economics. Unlike classical game dynamics, the study finds that uncertainty can reverse the direction of system evolution, and generate rich dynamical behaviors such as multistability and periodic oscillation limit rings. This study reveals the significant impact of uncertainty on the evolutionary dynamics and the complexity of collective behaviors.

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王龙,王国丞,苏奇.鲁棒博弈动力学: 分析与综合[J].控制与决策,2025,40(6):1761-1773

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  • 收稿日期:2024-11-05
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  • 在线发布日期: 2025-04-30
  • 出版日期: 2025-06-20
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