当前位置: X-MOL 学术Optimization › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
A decomposition algorithm for Nash equilibria in intersection management
Optimization ( IF 2.2 ) Pub Date : 2020-06-30 , DOI: 10.1080/02331934.2020.1786088
Andreas Britzelmeier 1 , Axel Dreves 1
Affiliation  

ABSTRACT

In this paper, we present a game-theoretic model, a new algorithmic framework with convergence theory, and numerical examples for the solution of intersection management problems. In our model, we consider autonomous vehicles that can communicate with each other in order to find individual optimal driving strategies through an intersection, without colliding with other vehicles. This results in coupled optimal control problems and we consider a generalized Nash equilibrium reformulation of the problem. Herein, we have individual differential equations, state and control constraints and additionally nonconvex shared constraints. To handle the nonconvexity we consider a partial penalty approach. To solve the resulting standard Nash equilibrium problem, we propose a decomposition method, where the selection of the players is controlled through penalty terms. The proposed method allows the prevention of a priori introduced hierarchies. Using dynamic programming, we prove convergence of our algorithm. Finally, we present numerical studies that show the effectiveness of the approach.



中文翻译:

交叉口管理中纳什均衡的一种分解算法

摘要

在本文中,我们提出了一个博弈论模型、一个具有收敛理论的新算法框架,以及用于解决交叉路口管理问题的数值例子。在我们的模型中,我们考虑了可以相互通信的自动驾驶车辆,以便在不与其他车辆碰撞的情况下通过交叉路口找到个人的最佳驾驶策略。这导致了耦合最优控制问题,我们考虑了该问题的广义纳什均衡重新表述。在这里,我们有单独的微分方程、状态和控制约束以及额外的非凸共享约束。为了处理非凸性,我们考虑部分惩罚方法。为了解决由此产生的标准纳什均衡问题,我们提出了一种分解方法,其中球员的选择是通过惩罚条款来控制的。所提出的方法允许防止先验引入的层次结构。使用动态规划,我们证明了算法的收敛性。最后,我们提出了数值研究,显示了该方法的有效性。

更新日期:2020-06-30
down
wechat
bug