Model reduction of controlled Fokker–Planck and Liouville–von Neumann equations

IF 1 Q3 Engineering

Journal of Computational Dynamics Pub Date : 2017-06-26 DOI:10.3934/jcd.2020001

P. Benner, T. Breiten, C. Hartmann, B. Schmidt

引用次数: 1

Abstract

Model reduction methods for bilinear control systems are compared by means of practical examples of Liouville-von Neumann and Fokker--Planck type. Methods based on balancing generalized system Gramians and on minimizing an H2-type cost functional are considered. The focus is on the numerical implementation and a thorough comparison of the methods. Structure and stability preservation are investigated, and the competitiveness of the approaches is shown for practically relevant, large-scale examples.

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控制Fokker-Planck和Liouville-von Neumann方程的模型简化

通过刘维尔-冯-诺伊曼型和福克-普朗克型的实例，比较了双线性控制系统的模型约简方法。考虑了基于平衡广义系统格律和最小化h2型代价泛函的方法。重点是数值实现和方法的全面比较。对结构和稳定性保持进行了研究，并在实际相关的大型实例中证明了这些方法的竞争力。

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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来源期刊

Journal of Computational Dynamics Engineering-Computational Mechanics

CiteScore

2.30

自引率

10.00%

发文量

期刊介绍： JCD is focused on the intersection of computation with deterministic and stochastic dynamics. The mission of the journal is to publish papers that explore new computational methods for analyzing dynamic problems or use novel dynamical methods to improve computation. The subject matter of JCD includes both fundamental mathematical contributions and applications to problems from science and engineering. A non-exhaustive list of topics includes * Computation of phase-space structures and bifurcations * Multi-time-scale methods * Structure-preserving integration * Nonlinear and stochastic model reduction * Set-valued numerical techniques * Network and distributed dynamics JCD includes both original research and survey papers that give a detailed and illuminating treatment of an important area of current interest. The editorial board of JCD consists of world-leading researchers from mathematics, engineering, and science, all of whom are experts in both computational methods and the theory of dynamical systems.