Stochastic Nonlinear Control via Finite-Dimensional Spectral Dynamics Embedding

• 成果类型: Article
• 署名作者: Ren, Zhaolin; Ren, Tongzheng; Ma, Haitong; Li, Na; Dai, Bo
• 署名单位: Harvard University; University of Texas System; University of Texas Austin
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3580296
• 发表日期: 2025
• 关键词: KOOPMAN OPERATOR

摘要

This article proposes an approach, spectral dynamics embedding control, to optimal control for nonlinear stochastic systems. This method reveals an infinite-dimensional feature representation induced by the system's nonlinear stochastic dynamics, enabling a linear representation of the state-action value function. For practical implementation, this representation is approximated using finite-dimensional truncations, specifically via two prominent kernel approximation methods: random feature truncation and Nystrom approximation. To characterize the effectiveness of these approximations, we provide an in-depth theoretical analysis to characterize the approximation error arising from the finite-dimension truncation and statistical error due to finite-sample approximation in both policy evaluation and policy optimization. Empirically, our algorithm performs favorably against existing stochastic control algorithms on several benchmark problems.