Koopman operator dynamical models: Learning, analysis and control

被引:57
|
作者
Bevanda, Petar [1 ]
Sosnowski, Stefan [1 ]
Hirche, Sandra [1 ]
机构
[1] Tech Univ Munich, Dept Elect & Comp Engn, Informat Oriented Control, D-80333 Munich, Germany
基金
欧盟地平线“2020”;
关键词
Koopman operator; Dynamical models; Representation learning; System analysis; Data-based control; NONLINEAR-SYSTEMS; SPECTRAL PROPERTIES; STABILITY ANALYSIS; REDUCTION; IDENTIFICATION; LINEARIZATION; DECOMPOSITION;
D O I
10.1016/j.arcontrol.2021.09.002
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
The Koopman operator allows for handling nonlinear systems through a globally linear representation. In general, the operator is infinite-dimensional - necessitating finite approximations - for which there is no overarching framework. Although there are principled ways of learning such finite approximations, they are in many instances overlooked in favor of, often ill-posed and unstructured methods. Also, Koopman operator theory has long-standing connections to known system-theoretic and dynamical system notions that are not universally recognized. Given the former and latter realities, this work aims to bridge the gap between various concepts regarding both theory and tractable realizations. Firstly, we review data-driven representations (both unstructured and structured) for Koopman operator dynamical models, categorizing various existing methodologies and highlighting their differences. Furthermore, we provide concise insight into the paradigm's relation to system-theoretic notions and analyze the prospect of using the paradigm for modeling control systems. Additionally, we outline the current challenges and comment on future perspectives.
引用
收藏
页码:197 / 212
页数:16
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