Numerical solution of optimal control problems for linear systems of ordinary differential equations-Reference-Cited by-同舟云学术

Numerical solution of optimal control problems for linear systems of ordinary differential equations

Published:2024-08-01 Issue:4 Volume:39 Page:175-185
ISSN:0927-6467
Container-title:Russian Journal of Numerical Analysis and Mathematical Modelling
language:en
Short-container-title:

Author:

Chechkin Ivan G.¹²,Demyanko Kirill V.¹³,Nechepurenko Yuri M.¹³

Affiliation:

1. Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences , Moscow , Russia

2. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics , Moscow , Russia

3. Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences , Moscow , Russia

Abstract

Abstract An original numerical matrix algorithm aimed at solving the optimal control problems for linear systems of ordinary differential equations with constant coefficients is proposed. The work of the algorithm is demonstrated with the problem, which consists in generating a given small disturbance of the Poiseuille flow in an infinite duct by blowing and suction through the walls. The costs of creating the leading modes and optimal disturbances are compared, which is of independent interest.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/rnam-2024-0017/pdf

Reference14 articles.

1. V. M. Alekseev, V. M. Tikhomirov, and S. V. Fomin, Optimal Control. Springer, New York, 1987.

2. E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, and D. Sorensen, LAPACK Users Guide. SIAM, Philadelphia, 1992.

3. A. V. Boiko, A. V. Dovgal, G. R. Grek, and V. V. Kozlov, Physics of Transitional Shear Flows. Springer, Berlin, 2012.

4. A. V. Boiko and Yu. M. Nechepurenko, Numerical spectral analysis of temporal stability of laminar duct flows with constant cross sections. J. Comput. Math. Math. Phys. 48 (2008), No. 10, 1–17.

5. A. V. Boiko and Yu. M. Nechepurenko, Numerical study of stability and transient phenomena of Poiseuille flows in ducts of square cross-sections. Russ. J. Numer. Anal. Math. Modelling 24 (2009), No. 3, 193–205.