线性系统的集合反馈镇定

IF 1.7 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2025-08-07 DOI:10.1007/s00245-025-10288-w

Philipp A. Guth, Karl Kunisch, Sérgio S. Rodrigues

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引用次数: 0

摘要

研究了具有参数相关系统矩阵的线性控制系统的镇定问题。提出并分析了一种基于Riccati的反馈机制。它是通过训练集参数的集合来构造的。这个单一的反馈稳定了训练集的所有系统以及它附近的系统。此外，它相对于来自训练集的每个参数的最优反馈的次优性可以量化。

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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Ensemble Feedback Stabilization of Linear Systems

Stabilization of linear control systems with parameter-dependent system matrices is investigated. A Riccati based feedback mechanism is proposed and analyzed. It is constructed by means of an ensemble of parameters from a training set. This single feedback stabilizes all systems of the training set and also systems in its vicinity. Moreover its suboptimality with respect to optimal feedback for each single parameter from the training set can be quantified.

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.