带有状态和控制依赖噪声的无限时域逆线性二次微分博弈
Infinite-Horizon Inverse Linear-Quadratic Differential Games with State- and Control-Dependent Noise
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中文总结 AI 辅助
本文针对带有状态和控制依赖噪声的N玩家无限时域线性二次微分博弈，推导线性反馈纳什均衡的充要条件及耦合随机代数黎卡提方程的核表示，求解逆问题并通过数值结果验证，凸显其固有模糊性。
中文摘要 AI 辅助
本文提出一种方法，用于求解带有状态和控制依赖噪声的N玩家无限时域线性二次（LQ）微分博弈的逆问题。针对该随机场景，我们推导了线性反馈纳什均衡的充要条件，其形式为耦合的随机代数黎卡提方程。随后，我们推导了这些方程的核表示，以明确刻画与观测到的均衡轨迹一致的所有玩家成本函数参数组合的集合，从而求解相关逆问题。数值结果验证了该方法并确认了理论发现，凸显了逆问题固有的模糊性。
英文摘要
This paper presents a method to solve the inverse problem for N-player infinite-horizon linear-quadratic (LQ) differential games with state- and control-dependent noise. For this stochastic setting, we derive necessary and sufficient conditions for linear feedback Nash equilibria, which take the form of coupled stochastic algebraic Riccati equations. We then derive a kernel representation of these equations to explicitly characterize the set of all cost function parameter combinations across players that are consistent with observed equilibrium trajectories, thereby solving the associated inverse problem. Numerical results illustrate the approach and confirm the theoretical findings, highlighting the inherent ambiguity of the inverse problem.
