Probabilistic reachable sets of stochastic nonlinear systems with contextual uncertainties

IF 4.8 2区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS
Xun Shen , Ye Wang , Kazumune Hashimoto , Yuhu Wu , Sebastien Gros
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引用次数: 0

Abstract

Validating and controlling safety-critical systems in uncertain environments necessitates probabilistic reachable sets of future state evolutions. The existing methods of computing probabilistic reachable sets normally assume that stochastic uncertainties are independent of system states, inputs, and other environment variables. However, this assumption falls short in many real-world applications, where the probability distribution governing uncertainties depends on these variables, referred to as contextual uncertainties. This paper addresses the challenge of computing probabilistic reachable sets of stochastic nonlinear states with contextual uncertainties by seeking minimum-volume polynomial sublevel sets with contextual chance constraints. The formulated problem cannot be solved by the existing sample-based approximation method since the existing methods do not consider conditional probability densities. To address this, we propose a consistent sample approximation of the original problem by leveraging conditional density estimation and resampling. The obtained approximate problem is a tractable optimization problem. Additionally, we prove the proposed sample-based approximation’s almost uniform convergence, showing that it gives the optimal solution almost consistently with the original ones. Through a numerical example, we evaluate the effectiveness of the proposed method against existing approaches, highlighting its capability to significantly reduce the bias inherent in sample-based approximation without considering a conditional probability density.
具有上下文不确定性的随机非线性系统的概率可达集
在不确定环境中验证和控制安全关键系统需要未来状态演化的概率可达集。现有的计算概率可达集的方法通常假设随机不确定性与系统状态、输入和其他环境变量无关。然而,这个假设在许多现实世界的应用中是不够的,在这些应用中,控制不确定性的概率分布取决于这些变量,称为上下文不确定性。本文通过寻找具有上下文机会约束的最小体积多项式子水平集,解决了具有上下文不确定性的随机非线性状态的概率可达集的计算问题。由于现有的基于样本的近似方法没有考虑条件概率密度,因此无法解决公式问题。为了解决这个问题,我们通过利用条件密度估计和重采样提出了原始问题的一致样本近似。所得到的近似问题是一个可处理的优化问题。此外,我们还证明了所提出的基于样本的近似几乎一致收敛,表明它给出的最优解与原始解几乎一致。通过一个数值例子,我们评估了所提出的方法与现有方法的有效性,突出了其在不考虑条件概率密度的情况下显著降低基于样本的近似固有偏差的能力。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Automatica
Automatica 工程技术-工程:电子与电气
CiteScore
10.70
自引率
7.80%
发文量
617
审稿时长
5 months
期刊介绍: Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field. After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience. Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.
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