Application of the fixed points method for the problems of dynamic systems optimization on parameters and initial conditions // BSU Bulletin. Mathematics, Informatics. - 2016. №1. . - С. 38-48.

Application of the fixed points method for the problems of dynamic systems optimization on parameters and initial conditions

Работа выполнена при финансовой поддержке РФФИ, проект № 15-01-03680-а; МОН РФ, проект №3808

DOI: 10.18101/2304-5728-2016-1-38-48 UDK: 517.977

In the article we have proposed the method for continual improvement of control parameters of dynamic systems. It is based on the solution of con- structed fixed point problem defined by the control operator. Application of the method is exemplified by the problem of identification the parameters and ini- tial conditions of a dynamical system.

dynamic system, parametric optimization, fixed point problem.

1. Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mishchenko E.

Matematicheskaya teoriya optimal'nykh protsessov [The Mathematical Theory of Optimal Processes]. Moscow: Nauka Publ., 1976. 392 p.

2. Buldaev A. S., Khishektueva I.-Kh. D. Metod nepodvizhnykh tochek v zadachakh parametricheskoi optimizatsii sistem [Method of Fixed Points in Problems of Systems Parametric Optimization]. Avtomatika i telemekhanika – Automation and Telecontrol. 2013. No. 12. Pp. 5–15.

3. Srochko V. A. Iteratsionnye metody resheniya zadach optimal'nogo upravleniya [Iterative Methods for Solving Optimal Control Problems]. Mos- cow: Fizmatlit Publ., 2000. 160 p.

4. Buldaev A. S. Metody vozmushchenii v zadachakh uluchsheniya i opti- mizatsii upravlyaemykh system [Perturbation Methods in Problems of Im- provement and Optimization of Control Systems]. Buryat State University Publ., 2008. 260 p.

5. Samarskii A. A., Gulin A. V. Chislennye metody [Numerical Methods]. Moscow: Nauka Publ., 1989. 432 p.