用于非线性系统识别的占位核方法

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-06-11 DOI:10.1137/19m127029x

Joel A. Rosenfeld, Benjamin P. Russo, Rushikesh Kamalapurkar, Taylor T. Johnson

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引用次数: 0

摘要

SIAM 控制与优化期刊》第 62 卷第 3 期第 1643-1668 页，2024 年 6 月。摘要本手稿提出了一种新的非线性系统辨识方法，利用密集定义的Liouville算子和一种新的 "核 "函数（代表重现核希尔伯特空间（RKHS）上的积分函数，称为占位核）。手稿深入探讨了连续函数 RKHS 上下文中的占位核概念，并建立了 RKHS 上的刘维尔算子，为这种无界算子的特定示例找到了几个密集域。这两个概念的结合可以将动态系统嵌入到 RKHS 中，从而利用函数论工具来研究此类系统。通过这一框架，非线性动态系统的轨迹可被视为非线性系统识别程序的基本数据单元。这种非线性系统识别方法不仅能准确识别动态系统的参数，还能对噪声表现出一定的鲁棒性。

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The Occupation Kernel Method for Nonlinear System Identification

SIAM Journal on Control and Optimization, Volume 62, Issue 3, Page 1643-1668, June 2024.
Abstract. This manuscript presents a novel approach to nonlinear system identification leveraging densely defined Liouville operators and a new “kernel” function that represents an integration functional over a reproducing kernel Hilbert space (RKHS) dubbed an occupation kernel. The manuscript thoroughly explores the concept of occupation kernels in the contexts of RKHSs of continuous functions and establishes Liouville operators over RKHS, where several dense domains are found for specific examples of this unbounded operator. The combination of these two concepts allows for the embedding of a dynamical system into an RKHS, where function-theoretic tools may be leveraged for the examination of such systems. This framework allows for trajectories of a nonlinear dynamical system to be treated as a fundamental unit of data for a nonlinear system identification routine. The approach to nonlinear system identification is demonstrated to identify parameters of a dynamical system accurately while also exhibiting a certain robustness to noise.

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来源期刊

SIAM Journal on Control and Optimization 数学-应用数学

CiteScore

4.00

自引率

4.50%

发文量

143

审稿时长

12 months

期刊介绍： SIAM Journal on Control and Optimization (SICON) publishes original research articles on the mathematics and applications of control theory and certain parts of optimization theory. Papers considered for publication must be significant at both the mathematical level and the level of applications or potential applications. Papers containing mostly routine mathematics or those with no discernible connection to control and systems theory or optimization will not be considered for publication. From time to time, the journal will also publish authoritative surveys of important subject areas in control theory and optimization whose level of maturity permits a clear and unified exposition. The broad areas mentioned above are intended to encompass a wide range of mathematical techniques and scientific, engineering, economic, and industrial applications. These include stochastic and deterministic methods in control, estimation, and identification of systems; modeling and realization of complex control systems; the numerical analysis and related computational methodology of control processes and allied issues; and the development of mathematical theories and techniques that give new insights into old problems or provide the basis for further progress in control theory and optimization. Within the field of optimization, the journal focuses on the parts that are relevant to dynamic and control systems. Contributions to numerical methodology are also welcome in accordance with these aims, especially as related to large-scale problems and decomposition as well as to fundamental questions of convergence and approximation.