研究控制误差下博弈策略的最优修正方法，提升实际执行中的性能。
Optimal Modified Feedback Strategies in LQ Games under Control Imperfections
- 通过可测偏差动态构建补偿策略，修正执行误差影响
- 在小偏差下，新策略局部优于未补偿的均衡反馈
- 适用于存在延迟或执行误差的工程博弈场景
博弈论与纳什均衡已广泛应用于多个工程领域。然而，扰动、延迟和执行器限制等实际问题会阻碍纳什均衡策略的精确实施。本文研究这些实现缺陷对双人有限时域线性二次（LQ）非零和博弈中轨迹与成本的影响。具体分析单个玩家在各阶段测量或估计的微小偏差如何影响状态轨迹及对方成本。为缓解此影响，通过将可测偏差动态加入名义博弈，为受影响玩家构造补偿律。所得策略被证明在因果仿射策略类中为最优，且在偏差足够小时，局部优于未补偿的均衡反馈策略。文中提供严谨分析与证明，并通过典型数值例子验证方法有效性。
原文摘要 · Abstract (English)
Game-theoretic approaches and Nash equilibrium have been widely applied across various engineering domains. However, practical challenges such as disturbances, delays, and actuator limitations can hinder the precise execution of Nash equilibrium strategies. This work investigates the impact of such implementation imperfections on game trajectories and players' costs in the context of a two-player finite-horizon linear quadratic (LQ) nonzero-sum game. Specifically, we analyze how small deviations by one player, measured or estimated at each stage affect the state trajectory and the other player's cost. To mitigate these effects, we construct a compensation law for the influenced player by augmenting the nominal game with the measurable deviation dynamics. The resulting policy is shown to be optimal within a causal affine policy class, and, for sufficiently small deviations, it locally outperforms the uncompensated equilibrium-derived feedback. Rigorous analysis and proofs are provided, and the effectiveness of the proposed approach is demonstrated through a representative numerical example.
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