Convexified Open-Loop Stochastic Optimal Control for Linear Systems With Log-Concave Disturbances

• 成果类型: Article
• 署名作者: Sivaramakrishnan, Vignesh; Vinod, Abraham P.; Oishi, Meeko M. K.
• 署名单位: University of New Mexico
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3284534
• 发表日期: 2024
• 页码: 1249-1256
• 关键词: Linear systems; mathematical programming; optimal control; Stochastic systems

摘要

In this article, we consider open-loop solutions to the stochastic optimal control of a linear dynamical system with an additive non-Gaussian, log-concave disturbance. We propose a novel, sampling-free approach, based on characteristic functions and convex optimization, to cast the stochastic optimal control problem as a difference-of-convex program. Our method invokes higher moments, resulting in less conservatism compared to moment-based approaches. We employ piecewise affine approximations and the convex-concave procedure for efficient solution via standard conic solvers. We demonstrate that the proposed solution is competitive with sampling- and moment-based approaches, without compromising probabilistic constraints.