标题： 求解线性二次动态博弈中单调变分不等式的Douglas-Rachford分裂方法 显示英文标题

标题： A Douglas-Rachford Splitting Method for Solving Monotone Variational Inequalities in Linear-quadratic Dynamic Games

摘要： 本文研究了具有二次目标函数的约束线性动态博弈问题，这类问题可以表示为仿射变分不等式。 通过利用问题的结构，我们应用Douglas-Rachford分裂方法，该方法生成了一个具有线性收敛速度的求解算法。 该方法的快速收敛性使得滚动时域控制架构成为可能。 此外，我们证明了相关的变分不等式在吸引子附近的某个邻域内存在闭式解，从而进一步减少了计算时间。 最后，我们在自动驾驶应用中通过数值实验对所提出的方法进行了基准测试。 显示英文摘要

摘要： This paper considers constrained linear dynamic games with quadratic objective functions, which can be cast as affine variational inequalities. By leveraging the problem structure, we apply the Douglas-Rachford splitting, which generates a solution algorithm with linear convergence rate. The fast convergence of the method enables receding-horizon control architectures. Furthermore, we demonstrate that the associated VI admits a closed-form solution within a neighborhood of the attractor, thus allowing for a further reduction in computation time. Finally, we benchmark the proposed method via numerical experiments in an automated driving application.