不确定条件下安全稳定控制的分布鲁棒Lyapunov-Barrier网络

IF 3.2 Q3 Mathematics
Ali Baheri
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引用次数: 0

摘要

本文解决了具有不确定参数的非线性控制系统如何同时实现稳定性和安全性的问题。本文提出了分布鲁棒李雅普诺夫-屏障网络(dr - lbn),这是一种将控制李雅普诺夫函数、控制屏障函数和分布鲁棒优化结合在一起的新框架。通过基于wasserstein的模糊集对参数不确定性建模,该方法为安全集的渐近稳定性和前向不变性提供了高概率保证,即使不确定性的真实分布是未知的或从训练转移到部署。我们形式化了概率稳定性、李雅普诺夫函数和势垒函数的普遍逼近以及样本复杂性的关键理论结果。在数值评估中,DR-LBN方法在安全裕度、收敛速度和控制努力方面优于简单的基线控制器和最坏情况鲁棒分布方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Distributionally robust Lyapunov–Barrier Networks for safe and stable control under uncertainty
This paper addresses the challenge of simultaneously achieving stability and safety in nonlinear control systems subject to uncertain parameters. We propose distributionally robust Lyapunov–Barrier networks (DR-LBNs), a novel framework that unifies control Lyapunov functions, control barrier functions, and distributionally robust optimization. By modeling parametric uncertainties through a Wasserstein-based ambiguity set, proposed approach offers high-probability guarantees on both asymptotic stability and forward invariance of a safe set, even when the true distribution of uncertainties is unknown or shifts from training to deployment. We formalize key theoretical results on probabilistic stability, universal approximation of Lyapunov and barrier functions, and sample complexity. In numerical evaluations, the DR-LBN approach outperforms both a simple baseline controller and a worst-case robust distribution method in terms of safety margins, convergence speed, and control effort.
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来源期刊
Results in Control and Optimization
Results in Control and Optimization Mathematics-Control and Optimization
CiteScore
3.00
自引率
0.00%
发文量
51
审稿时长
91 days
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