用最优传输方法实现数据驱动的分布精准调控，适用于未知动态系统。
Data-Driven Density Steering via the Gromov-Wasserstein Optimal Transport Distance
- 基于格罗莫夫-沃瑟斯坦距离建模状态分布演化
- 将控制问题转为可解的凸差分规划，支持高效求解
- 适合有充分实验数据的控制系统设计与优化
我们采用格罗莫夫-沃瑟斯坦最优传输距离，解决数据驱动的机会约束密度调控问题。系统为未知线性控制递推模型，假设具备充分丰富的预运行输入输出数据。初始状态为高斯混合分布，终端状态需匹配指定高斯分布。我们将优化控制问题重构为凸差分规划，并证明可通过DC算法高效、可计算地求解。数值实验验证了该方法在多种数据驱动方案下的有效性。
原文摘要 · Abstract (English)
We tackle the data-driven chance-constrained density steering problem using the Gromov-Wasserstein metric. The underlying dynamical system is an unknown linear controlled recursion, with the assumption that sufficiently rich input-output data from pre-operational experiments are available. The initial state is modeled as a Gaussian mixture, while the terminal state is required to match a specified Gaussian distribution. We reformulate the resulting optimal control problem as a difference-of-convex program and show that it can be efficiently and tractably solved using the DC algorithm. Numerical results validate our approach through various data-driven schemes.
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