High-Dimensional Optimal Density Control with Wasserstein Metric Matching
High-Dimensional Optimal Density Control with Wasserstein Metric Matching
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DOI：
10.1109/cdc49753.2023.10384042
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发表时间：
2023-07
期刊：
影响因子：
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通讯作者：
Shaojun Ma;Mengxue Hou;X. Ye;Haomin Zhou
中科院分区：
文献类型：
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作者：
Shaojun Ma;Mengxue Hou;X. Ye;Haomin Zhou
我们提出了一种新的计算框架，在高维状态空间的密度控制。所考虑的动力系统由大量的不可区分的代理，其行为可以集体建模为一个时间演变的概率分布。我们的目标是引导代理从一个初始分布，以达到（或近似）在一个固定的时间范围内以最小的成本给定的目标分布没有冲突。为了解决这个问题，我们建议将漂移建模为非线性降阶模型，例如深度网络，并使用Wasserstein度量在终端时间严格或近似地执行与目标分布的匹配。由此产生的鞍点问题可以通过有效的数值算法来解决，该算法利用了深度网络的出色表示能力和快速自动微分来解决这个具有挑战性的高维控制问题。各种数值实验进行了证明我们的方法的性能。
We present a novel computational framework for density control in high-dimensional state spaces. The considered dynamical system consists of a large number of indistinguishable agents whose behaviors can be collectively modeled as a time-evolving probability distribution. The goal is to steer the agents without collision from an initial distribution to reach (or approximate) a given target distribution within a fixed time horizon at minimum cost. To tackle this problem, we propose to model the drift as a nonlinear reduced-order model, such as a deep network, and enforce the matching to the target distribution at terminal time either strictly or approximately using the Wasserstein metric. The resulting saddle-point problem can be solved by an effective numerical algorithm that leverages the excellent representation power of deep networks and fast automatic differentiation for this challenging high-dimensional control problem. A variety of numerical experiments were conducted to demonstrate the performance of our method.