论文标题
受约束非线性动态游戏的一阶算法
First-Order Algorithms for Constrained Nonlinear Dynamic Games
论文作者
论文摘要
本文介绍了非零和非线性约束动态游戏的算法，并提供了完整的信息。当多个具有行动限制和不同目标的玩家与同一动态系统相互作用时，这些问题就会出现。它们对包括经济学，国防和能源系统在内的广泛应用进行了建模。我们展示了如何利用投影梯度和道格拉斯·拉赫福德（DR）分裂方法中的时间结构。所得算法以线性速率在本地收敛到开环NASH平衡（OLNE）。此外，我们扩展了舞台牛顿方法，以找到围绕奥尔恩的本地反馈政策。在线性动力学和多面体约束中，我们表明该局部反馈控制器是近似反馈NASH平衡（FNE）。提供了数值示例。
This paper presents algorithms for non-zero sum nonlinear constrained dynamic games with full information. Such problems emerge when multiple players with action constraints and differing objectives interact with the same dynamic system. They model a wide range of applications including economics, defense, and energy systems. We show how to exploit the temporal structure in projected gradient and Douglas-Rachford (DR) splitting methods. The resulting algorithms converge locally to open-loop Nash equilibria (OLNE) at linear rates. Furthermore, we extend stagewise Newton method to find a local feedback policy around an OLNE. In the of linear dynamics and polyhedral constraints, we show that this local feedback controller is an approximated feedback Nash equilibrium (FNE). Numerical examples are provided.
