AI中文摘要
从协同制导到碰撞避免等安全关键多智能体系统，通常必须在硬截止时间前达成协调决策，而非仅仅最终收敛。本文提出首个全分布式算法，用于在用户预设时间$T$内求解广义纳什均衡（GNE）问题（一种具有共享耦合约束和一般成本耦合的非合作博弈），该时间独立于初始条件。其基础是建立在优化李雅普诺夫函数框架上的集中式预设时间结果，并通过非归一化Hessian-梯度反馈实现，选择该反馈是因为与牛顿和归一化Hessian-梯度实现不同，它自然地分解为每个智能体的计算。分布式实现该反馈要求每个智能体同时运行三个耦合过程：全局状态的预设时间观测器、局部优化律以及强制变分GNE共享乘子的对偶一致性机制。它们的同步运行是核心难点，因为优化不断位移观测器跟踪的状态，而估计误差污染驱动优化的梯度。我们通过一种多速率增益调度解决该耦合，其中观测器和一致性层比优化层严格更快收缩，使得每个误差分量在$T$时刻精确消失。Fischer-Burmeister重构保持设计无投影，同时在截止时间强制执行约束。针对Cournot博弈和时间关键传感器覆盖问题的数值结果验证了该方法，并展示了其作为时间关键自主性求解器在环的应用。
英文摘要
Safety-critical multi-agent systems, from cooperative guidance to collision avoidance, must often reach a coordinated decision by a hard deadline rather than merely converge to one eventually. This paper proposes the first fully distributed algorithm that solves the generalized Nash equilibrium (GNE) problem, a non-cooperative game with shared coupling constraints and general cost coupling, at a user-prescribed time $T$ independent of initial conditions. The foundation is a centralized, prescribed-time result built on the optimization Lyapunov function framework and implemented via unnormalized Hessian-gradient feedback, chosen because, unlike the Newton and normalized Hessian-gradient realizations, it naturally splits into per-agent computations. Distributing this feedback requires each agent to run three coupled processes simultaneously: a prescribed-time observer of the global state, a local optimization law, and a dual-consensus mechanism that enforces the shared multipliers of the variational GNE. Their simultaneous operation is the core difficulty, as the optimization continually displaces the states the observers track, while estimation errors corrupt the gradients that drive the optimization. We resolve this coupling with a multi-rate gain schedule whose observer and dual-consensus layers contract strictly faster than the optimization layer, so that every error component vanishes exactly at $T$. A Fischer-Burmeister reformulation keeps the design projection-free while enforcing the constraints at the deadline. Numerical results for a Cournot game and a time-critical sensor-coverage problem validate the approach and demonstrate its use as a solver-in-the-loop for time-critical autonomy.
