Newton’s Method and Differential Dynamic Programming for Unconstrained Nonlinear Dynamic Games
Newton’s Method and Differential Dynamic Programming for Unconstrained Nonlinear Dynamic Games
复制标题
无约束非线性动态博弈的牛顿法和微分动态规划
DOI：
10.1109/cdc40024.2019.9029237
复制
发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Andrew G. Lamperski
中科院分区：
文献类型：
--
作者：
Bolei Di;Andrew G. Lamperski
当具有不同目标的多个代理选择控制输入到动态系统时，动态博弈就产生了。然而，与单智能体控制问题相比，动态博弈的计算方法相对有限。只有非常专业的动态对策才能精确求解，因此需要近似算法。在这篇文章中，我们展示了如何将递归牛顿算法和微分动态规划(DDP)推广到完全信息非零和动态对策的情况。我们证明了牛顿法和DDP的迭代足够接近，使得DDP继承了牛顿法的二次收敛速度。
Dynamic games arise when multiple agents with differing objectives choose control inputs to a dynamic system. However, compared to single-agent control problems, the computational methods for dynamic games are relatively limited. Only very specialized dynamic games can be solved exactly, so approximation algorithms are required. In this paper, we show how to extend a recursive Newton algorithm and differential dynamic programming (DDP) to the case of full-information non-zero sum dynamic games. We show that the iterates of Newton’s method and DDP are sufficiently close for DDP to inherit the quadratic convergence rate of Newton’s method.
影响因子：
1.5
作者：
Ioannis Exarchos;Evangelos A. Theodorou;P. Tsiotras
通讯作者：
Ioannis Exarchos;Evangelos A. Theodorou;P. Tsiotras