连续时间基本定理及其在数据驱动最优控制中的应用

IF 2.1 3区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

Systems & Control Letters Pub Date : 2024-10-30 DOI:10.1016/j.sysconle.2024.105950

Philipp Schmitz , Timm Faulwasser , Paolo Rapisarda , Karl Worthmann

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引用次数: 0

摘要

离散时间和连续时间系统的数据驱动控制是一项极具研究价值的课题。在本文中，我们利用输入输出数据探索连续时间线性系统的数据驱动最优控制。基于密度结果，我们严格推导出了系统行为元素的有限阶多项式近似误差边界。为此，我们利用了可控系统的潜变量和平面输出之间的联系。结合 Willems 等人的连续时间对应基本定理，我们描述了数据驱动的线性-二次方最优控制中多项式近似产生的次最优性。最后，我们利用一个数值示例来说明我们的结果。

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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A continuous-time fundamental lemma and its application in data-driven optimal control

Data-driven control of discrete-time and continuous-time systems is of tremendous research interest. In this paper, we explore data-driven optimal control of continuous-time linear systems using input–output data. Based on a density result, we rigorously derive error bounds for finite-order polynomial approximations of elements of the system behavior. To this end, we leverage a link between latent variables and flat outputs of controllable systems. Combined with a continuous-time counterpart of Willems et al.’s fundamental lemma, we characterize the suboptimality resulting from polynomial approximations in data-driven linear–quadratic optimal control. Finally, we draw upon a numerical example to illustrate our results.

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来源期刊

Systems & Control Letters 工程技术-运筹学与管理科学

CiteScore

4.60

自引率

3.80%

发文量

144

审稿时长

6 months

期刊介绍： Founded in 1981 by two of the pre-eminent control theorists, Roger Brockett and Jan Willems, Systems & Control Letters is one of the leading journals in the field of control theory. The aim of the journal is to allow dissemination of relatively concise but highly original contributions whose high initial quality enables a relatively rapid review process. All aspects of the fields of systems and control are covered, especially mathematically-oriented and theoretical papers that have a clear relevance to engineering, physical and biological sciences, and even economics. Application-oriented papers with sophisticated and rigorous mathematical elements are also welcome.