Open-Loop Chance Constrained Stochastic Optimal Control via the One-Sided Vysochanskij-Petunin Inequality

• 成果类型: Article
• 署名作者: Pacula, Isabella; Oishi, Meeko
• 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.2024.3386460
• 发表日期: 2024
• 页码: 5383-5395
• 关键词: Arbitrary disturbances; chance constrained stochastic optimal control; multivehicle motion planning; stochastic linear systems

摘要

While many techniques have been developed for chance constrained stochastic optimal control with Gaussian disturbance processes, far less is known about computationally efficient methods to handle non-Gaussian processes. In this article, we develop a method for solving chance constrained stochastic optimal control problems for linear time-invariant systems with general additive disturbances with finite moments and unimodal chance constraints. We propose an open-loop control scheme for multivehicle planning, with both target sets and collision avoidance constraints. Our method relies on the one-sided Vysochanskij-Petunin inequality, a tool from statistics used to bound tail probabilities of unimodal random variables. Using the one-sided Vysochanskij-Petunin inequality, we reformulate each chance constraint in terms of the expectation and standard deviation. While the reformulated bounds are conservative with respect to the original bounds, they have a simple and closed form, and are amenable to difference of convex optimization techniques. We demonstrate our approach on a multisatellite rendezvous problem.