Singular linear-quadratic control problem for systems with linear delay
Abstract
A singular linear-quadratic optimization problem on the trajectories of non-autonomous linear differential equations with linear delay is considered. The peculiarity of this problem is the fact that this problem has no solution in the class of integrable controls. To ensure the existence of solutions is required to expand the class of controls including controls with impulse components. Dynamical systems with linear delay are used to describe the motion of pantograph from the current collector with electric traction, biology, etc. It should be noted that for practical problems fact singularity criterion of quality is quite commonly occurring, and therefore the study of these problems is surely important. For the problem under discussion optimal programming control contained impulse components at the initial and final moments of time is constructed under certain assumptions on the functional and the right side of the control system.
- Authors:
-
- Ural Federal University, 19 S. Mira, Ekaterinburg, 620002 (Russian Federation)
- Publication Date:
- OSTI Identifier:
- 22262767
- Resource Type:
- Journal Article
- Journal Name:
- AIP Conference Proceedings
- Additional Journal Information:
- Journal Volume: 1570; Journal Issue: 1; Conference: AMEE 13: 39. international conference on applications of mathematics in engineering and economics, Sozopol (Bulgaria), 8-13 Jun 2013; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; CONTROL SYSTEMS; DIFFERENTIAL EQUATIONS; INTEGRAL CALCULUS; OPTIMIZATION; PROGRAMMING; PULSES; SINGULARITY
Citation Formats
Sesekin, A. N., and Institute of Mathematics and Mechanics, Ural Division of Russian Academy of Sciences, 16 S. Kovalevskaya, Ekaterinburg, 620990. Singular linear-quadratic control problem for systems with linear delay. United States: N. p., 2013.
Web. doi:10.1063/1.4854765.
Sesekin, A. N., & Institute of Mathematics and Mechanics, Ural Division of Russian Academy of Sciences, 16 S. Kovalevskaya, Ekaterinburg, 620990. Singular linear-quadratic control problem for systems with linear delay. United States. https://doi.org/10.1063/1.4854765
Sesekin, A. N., and Institute of Mathematics and Mechanics, Ural Division of Russian Academy of Sciences, 16 S. Kovalevskaya, Ekaterinburg, 620990. 2013.
"Singular linear-quadratic control problem for systems with linear delay". United States. https://doi.org/10.1063/1.4854765.
@article{osti_22262767,
title = {Singular linear-quadratic control problem for systems with linear delay},
author = {Sesekin, A. N. and Institute of Mathematics and Mechanics, Ural Division of Russian Academy of Sciences, 16 S. Kovalevskaya, Ekaterinburg, 620990},
abstractNote = {A singular linear-quadratic optimization problem on the trajectories of non-autonomous linear differential equations with linear delay is considered. The peculiarity of this problem is the fact that this problem has no solution in the class of integrable controls. To ensure the existence of solutions is required to expand the class of controls including controls with impulse components. Dynamical systems with linear delay are used to describe the motion of pantograph from the current collector with electric traction, biology, etc. It should be noted that for practical problems fact singularity criterion of quality is quite commonly occurring, and therefore the study of these problems is surely important. For the problem under discussion optimal programming control contained impulse components at the initial and final moments of time is constructed under certain assumptions on the functional and the right side of the control system.},
doi = {10.1063/1.4854765},
url = {https://www.osti.gov/biblio/22262767},
journal = {AIP Conference Proceedings},
issn = {0094-243X},
number = 1,
volume = 1570,
place = {United States},
year = {Wed Dec 18 00:00:00 EST 2013},
month = {Wed Dec 18 00:00:00 EST 2013}
}