Geodesic
On a method for finding extremal controls in systems with constraints
The Bulletin of Irkutsk State University. Series Mathematics, Tome 30 (2019), pp. 16-30
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the class of controlled systems with constraints, the conditions for improving and optimality of control are constructed and analyzed in the form of fixed point problems. This form allows one to obtain enhanced necessary optimality conditions in comparison with the known conditions and makes it possible to apply and modify the theory and methods of fixed points to search for extreme controls in optimization problems of the class under consideration. Fixed-point problems are constructed using the transition to auxiliary optimal control problems without restrictions with Lagrange functionals. An iterative algorithm is proposed for constructing a relaxation sequence of admissible controls based on the solution of constructed fixed point problems. The considered algorithm is characterized by the properties of nonlocal improvement of admissible control and the fundamental possibility of rigorous improvement of non-optimal controls satisfying the known necessary optimality conditions, in contrast to gradient and other local methods. The conditions of convergence of the control sequence for the residual of fulfilling the necessary optimality conditions are substantiated. A comparative analysis of the computational and qualitative efficiency of the proposed iterative algorithm for finding extreme controls in a model problem with phase constraints is carried out.
Keywords: the controlled system with constraints, extreme controls, conditions for improving control, fixed point problem, iterative algorithm. 
@article{IIGUM_2019_30_a1,
     author = {A. S. Buldaev and I. D. Burlakov},
     title = {On a method for finding extremal controls in systems with constraints},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {16--30},
     year = {2019},
     volume = {30},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2019_30_a1/}
}
TY  - JOUR
AU  - A. S. Buldaev
AU  - I. D. Burlakov
TI  - On a method for finding extremal controls in systems with constraints
JO  - The Bulletin of Irkutsk State University. Series Mathematics
PY  - 2019
SP  - 16
EP  - 30
VL  - 30
UR  - http://geodesic.mathdoc.fr/item/IIGUM_2019_30_a1/
LA  - en
ID  - IIGUM_2019_30_a1
ER  - 
%0 Journal Article
%A A. S. Buldaev
%A I. D. Burlakov
%T On a method for finding extremal controls in systems with constraints
%J The Bulletin of Irkutsk State University. Series Mathematics
%D 2019
%P 16-30
%V 30
%U http://geodesic.mathdoc.fr/item/IIGUM_2019_30_a1/
%G en
%F IIGUM_2019_30_a1
A. S. Buldaev; I. D. Burlakov. On a method for finding extremal controls in systems with constraints. The Bulletin of Irkutsk State University. Series Mathematics, Tome 30 (2019), pp. 16-30. http://geodesic.mathdoc.fr/item/IIGUM_2019_30_a1/

[1] O. V. Bartenev, Fortran for Professionals. Mathematical Library IMSL, v. 2, Dialog-MIFI Publ., M., 2001, 320 pp. (in Russian)

[2] A. S. Buldaev, “Fixed-Point Methods Based on Projection Operations in Optimization Problems for Control Functions and parameters of Dynamical Systems”, Bulletin of the Buryat State University. Mathematics, Computer Science, 2017, no. 1, 38–54 (in Russian) | DOI

[3] A. S. Buldaev, Perturbation Methods in Improvement and Optimization Problems for Controllable Systems, Publishing House of the Buryat State University, Ulan-Ude, 2008, 260 pp. (in Russian)

[4] A. S. Buldaev, I. D. Burlakov, “About One Approach to Numerical Solution of Nonlinear Optimal Speed Problems”, Bulletin of the South Ural State University. Series Mathematical Modeling, Programming Computer Software, 11:4 (2018), 55–66 | DOI | MR

[5] A. S. Buldaev, I. Kh. Khishektueva, “The Fixed Point Method in ametric Optimization Problems for Systems”, Automation and Remote Control, 74:12 (2013), 1927–1934 | DOI | MR | Zbl

[6] N. I. Grachev, A. N. Filkov, The Solution of Optimal Control Problems in the DISO System, Publishing House of Computer Center of the Academy of Sciences USSR, M., 1986, 66 pp. (in Russian)

[7] A. A. Samarsky, A. V. Gulin, Numerical Nethods, Nauka, M., 1989, 432 pp. (in Russian)

[8] V. A. Srochko, Iterative Methods for Solving Optimal Control Problems, Fizmatlit, M., 2000, 160 pp. (in Russian)

[9] A. I. Tyatyushkin, Multi-Method Technology for Optimizing Controlled Systems, Nauka Publ., Novosibirsk, 2006, 343 pp. (in Russian)

[10] O. V. Vasiliev, Lectures on Optimization Methods, Publishing House of Irkutsk State University, Irkutsk, 1994, 340 pp. (in Russian)