约束微分博弈中基于模型预测控制的近似反馈纳什均衡及其上界保证
Approximate Feedback Nash Equilibria in Constrained Differential Games via Model Predictive Control with Upper Bound Guarantees
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中文总结 AI 辅助
本文提出一种基于模型预测控制的近似方法，通过求解有限时域开环博弈逼近约束微分博弈中的反馈纳什均衡，并给出无约束情形下轨迹偏差的解析上界，数值实验验证了其有效性。
中文摘要 AI 辅助
物理人机交互及其他多智能体控制场景需要能够在线适应的决策策略。微分博弈提供了一个原则性框架，其中每个智能体在预测其他智能体响应的同时优化自身目标。在许多应用中，相关的解概念是反馈纳什均衡（FNE），它产生时间一致的状态反馈策略。然而，计算FNE要求很高，并且在必须强制执行状态和输入约束时变得难以处理，这促使了对近似方法的需求。本文提出了一种模型预测控制（MPC）方法，通过重复求解有限时域开环博弈来近似无限时域FNE轨迹。引入了一种辅助博弈公式，用于选择预测时域和终端代价以近似反馈博弈的最优性条件。该方法通过约束开环博弈公式扩展到包含硬约束。对于无约束情形，推导了MPC诱导轨迹与FNE轨迹之间状态轨迹偏差的解析上界，从而实现了定量性能认证。数值示例说明了所提出方法相对于文献中基线方法的有效性。
英文摘要
Physical human--machine interaction and other multi-agent control settings require decision-making policies that adapt online. Differential games provide a principled framework where each agent optimizes an individual objective while anticipating the other's response. The relevant solution concept in many applications is the feedback Nash equilibrium (FNE), which yields time-consistent state-feedback strategies. However, computing the FNE is demanding and becomes intractable when state and input constraints must be enforced, motivating the need for approximate methods. This paper presents a Model Predictive Control (MPC) approach that approximates infinite-horizon FNE trajectories through repeated solution of finite-horizon open-loop games. An auxiliary-game formulation is introduced that selects prediction horizons and terminal costs to approximate the feedback-game optimality conditions. The approach is extended to incorporate hard constraints via a constrained open-loop game formulation. For the unconstrained setting, an analytic upper bound on the state-trajectory deviation between the MPC-induced and FNE trajectories is derived, enabling quantitative performance certification. Numerical examples illustrate the effectiveness of the proposed method compared with baseline approaches from the literature.
