基于 RKHS 的数据驱动随机最优控制

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Abstract:This paper proposes a fully data-driven approach for optimal control of nonlinear control-affine systems represented by a stochastic diffusion. The focus is on the scenario where both the nonlinear dynamics and stage cost functions are unknown, while only a control penalty function and constraints are provided. To this end, we embed state probability densities into a reproducing kernel Hilbert space (RKHS) to leverage recent advances in operator regression, thereby identifying Markov transition operators associated with controlled diffusion processes. This operator learning approach integrates naturally with convex operator-theoretic Hamilton-Jacobi-Bellman recursions that scale linearly with state dimensionality, effectively solving a wide range of nonlinear optimal control problems. Numerical results demonstrate its ability to address diverse nonlinear control tasks, including the depth regulation of an autonomous underwater vehicle.

Subjects:	Optimization and Control (math.OC); Machine Learning (cs.LG); Systems and Control (eess.SY); Machine Learning (stat.ML)
Cite as:	arXiv:2407.16407 [math.OC]
	(or arXiv:2407.16407v3 [math.OC] for this version)
	https://doi.org/10.48550/arXiv.2407.16407 arXiv-issued DOI via DataCite
Journal reference:	Engineering Applications of Artificial Intelligence, 1 October 2026, Volume 181, Part 6, Article 115698
Related DOI:	https://doi.org/10.1016/j.engappai.2026.115698 DOI(s) linking to related resources

Submission history

From: Nicolas Hoischen [view email]
[v1] Tue, 23 Jul 2024 11:53:03 UTC (5,699 KB)
[v2] Fri, 31 Oct 2025 15:27:52 UTC (10,601 KB)
[v3] Fri, 9 Oct 2026 09:21:22 UTC (10,604 KB)