Optimal stochastic forcings for sensitivity analysis of linear dynamical systems-Reference-Cited by-同舟云学术

Optimal stochastic forcings for sensitivity analysis of linear dynamical systems

Published:2022-04-01 Issue:2 Volume:37 Page:111-118
ISSN:0927-6467
Container-title:Russian Journal of Numerical Analysis and Mathematical Modelling
language:en
Short-container-title:

Author:

Nechepurenko Yuri M.¹²,Zasko Grigory V.¹²

Affiliation:

1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences , Miusskaya sq. 4 , Moscow Russia

2. Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences , Gubkin str. 8 , Moscow , Russia

Abstract

Abstract The paper is devoted to the construction of optimal stochastic forcings for studying the sensitivity of linear dynamical systems to external perturbations. The optimal forcings are sought to maximize the Schatten norms of the response. As an example,we consider the problem of constructing the optimal stochastic forcing for the linear dynamical system arising from the analysis of large-scale structures in a stratified turbulent Couette flow.

Publisher

Walter de Gruyter GmbH

Subject

Modeling and Simulation,Numerical Analysis

Link

https://www.degruyter.com/document/doi/10.1515/rnam-2022-0009/pdf

Reference23 articles.

1. Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst (Eds.), Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide. SIAM, Philadelphia, 2000.

2. B. Bamieh and M. Dahleh, Energy amplification in channel flows with stochastic excitation. Phys. Fluids 13 (2001), 3258– 3269.

3. R. H. Bartels and G. W. Stewart, Solution of the matrix equation AX + XB = C. Commun. ACM 15 (1972), 820–826.

4. R. Bhatia, A note on the Lyapunov equation. Linear Alg. Appl. 259 (1997), 71–76.

5. R. Bhatia, Matrix Analysis. Springer-Verlag, New York, 1997.