论文标题
基于优化的激励和控制方案
Optimization-based incentivization and control scheme for autonomous traffic
论文作者
论文摘要
我们考虑了激励和最佳控制自动驾驶汽车以改善交通拥堵的问题。在我们的情况下，必须激励自动驾驶汽车才能参与交通改善。使用最佳传输的理论和方法，我们提出了一个受部分微分方程控制的动态的约束优化框架，以便我们可以最佳地选择一部分车辆，以激励和控制。 优化的目的是在空间域中获得车辆均匀分布。为了实现这一目标，我们考虑了两种类型的车辆密度处罚类型，一种是$ l^2 $成本，另一个是多尺寸的成本，通常用于流体混合问题。为了解决这个非凸优化问题，我们介绍了一种新型算法，该算法在解决凸优化问题和根据Lighthill-Whitham-Richards模型的情况下迭代了。我们执行数值模拟，这表明$ l^2 $成本的优化是无效的，而多尺度的优化是有效的。结果还表明，在实践中，将专用车道用于此类控制。
We consider the problem of incentivization and optimal control of autonomous vehicles for improving traffic congestion. In our scenario, autonomous vehicles must be incentivized in order to participate in traffic improvement. Using the theory and methods of optimal transport, we propose a constrained optimization framework over dynamics governed by partial differential equations, so that we can optimally select a portion of vehicles to be incentivized and controlled. The goal of the optimization is to obtain a uniform distribution of vehicles over the spatial domain. To achieve this, we consider two types of penalties on vehicle density, one is the $L^2$ cost and the other is a multiscale-norm cost, commonly used in fluid-mixing problems. To solve this non-convex optimization problem, we introduce a novel algorithm, which iterates between solving a convex optimization problem and propagating the flow of uncontrolled vehicles according to the Lighthill-Whitham-Richards model. We perform numerical simulations, which suggest that the optimization of the $L^2$ cost is ineffective while optimization of the multiscale norm is effective. The results also suggest the use of a dedicated lane for this type of control in practice.
