用核方法学习随机系统的最优控制，无需完整模型。
Kernel-Based Optimal Control: An Infinitesimal Generator Approach
- 在再生核希尔伯特空间中直接学习控制扩散的无穷小生成算子。
- 数据驱动求解，兼容现代凸算子哈密顿-雅可比-贝尔曼递推。
- 适合缺乏精确模型的复杂系统控制，如机器人与随机微分方程。
本文提出一种新型算子理论方法，用于在再生核希尔伯特空间中对非线性随机系统进行最优控制。该学习框架利用系统动态和阶段代价函数的数据样本，仅需提供控制惩罚项和约束条件。所提方法直接在无限维假设空间中学习受控随机扩散的无穷小生成算子。我们证明该方法可无缝集成到现代凸算子理论的哈密顿-雅可比-贝尔曼递推中，实现数据驱动的最优控制求解。此外，该学习框架包含无参数估计器对未受控无穷小生成算子的特殊情形。数值实验涵盖从合成微分方程到模拟机器人系统的多个场景，展示了其相较现代数据驱动方法和经典非线性规划方法的优势。
原文摘要 · Abstract (English)
This paper presents a novel operator-theoretic approach for optimal control of nonlinear stochastic systems within reproducing kernel Hilbert spaces. Our learning framework leverages data samples of system dynamics and stage cost functions, with only control penalties and constraints provided. The proposed method directly learns the infinitesimal generator of a controlled stochastic diffusion in an infinite-dimensional hypothesis space. We demonstrate that our approach seamlessly integrates with modern convex operator-theoretic Hamilton-Jacobi-Bellman recursions, enabling a data-driven solution to the optimal control problems. Furthermore, our learning framework includes nonparametric estimators for uncontrolled infinitesimal generators as a special case. Numerical experiments, ranging from synthetic differential equations to simulated robotic systems, showcase the advantages of our approach compared to both modern data-driven and classical nonlinear programming methods for optimal control.
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