基于延迟输出测量的静态映射安全牛顿极值搜索
Safe Newton-Based Extremum Seeking for Static Maps with Delayed Output Measurements
- School of Engineering and Computing, Christopher Newport University（克里斯托弗纽波特大学工程与计算学院）
- State University of Rio de Janeiro（里约热内卢州立大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出延迟安全牛顿极值搜索框架，通过无模型预测器和鲁棒CLF-CBF二次规划，在未知静态映射、安全约束及延迟测量下实现约束优化，并保证收敛与安全。
AI中文摘要：
本文提出了一种延迟安全牛顿极值搜索（SANES）框架，用于在未知安全约束下最小化未知静态映射。假设目标函数和安全测量受相同恒定时间延迟的影响。为补偿延迟测量，开发了一种无模型预测器，用于构建优化所需的量，包括标称牛顿极值搜索控制输入和用于制定控制李雅普诺夫函数（CLF）和控制障碍函数（CBF）条件的梯度信息。随后，制定了受参数更新约束的鲁棒CLF-CBF二次规划（QP），以明确考虑导数估计和预测误差。对于无延迟情况，鲁棒性裕度由极值搜索估计误差的界限导出；而对于延迟情况，裕度同时包含估计误差和预测误差。通过李雅普诺夫分析直接建立了标称牛顿极值搜索动力学的实际稳定性，从而在允许的参数集上提供收敛保证，而不完全依赖局部平均论证。随后推导了鲁棒CLF和CBF条件，以建立规定安全集的鲁棒子集的实用收敛和前向不变性。数值案例研究证明了所提出的SANES框架在未知目标和安全映射及延迟测量下实现约束优化的有效性。
英文摘要：
This work presents a delayed safe Newton-based extremum seeking (SANES) framework for minimizing an unknown static map subject to an unknown safety constraint. The objective and safety measurements are assumed to be affected by the same constant time delay. To compensate for delayed measurements, a model-free predictor is developed to construct the quantities required for optimization, including the nominal Newton-based extremum-seeking control input and the gradient information used to formulate control Lyapunov function (CLF) and control barrier function (CBF) conditions. Robust CLF--CBF quadratic programs (QPs), subject to parameter-update constraints, are then formulated to account explicitly for derivative-estimation and prediction errors. For the delay-free case, robustness margins are derived from bounds on the extremum-seeking estimation errors, whereas for the delayed case, the margins incorporate both estimation and prediction errors. Practical stability of the nominal Newton-based extremum-seeking dynamics is established directly through a Lyapunov analysis, thereby providing convergence guarantees over the admissible parameter set without relying exclusively on local averaging arguments. Robust CLF and CBF conditions are subsequently derived to establish practical convergence and forward invariance of a robust subset of the prescribed safe set. A numerical case study demonstrates the effectiveness of the proposed SANES framework in achieving constrained optimization despite unknown objective and safety maps and delayed measurements.
