BSU Bulletin. Mathematics, Informatics
Bibliographic description:
, NONLOCAL DESCENT METHOD AT A SET OF ADMISSIBLE CONTROLS IN OPTIMAL CONTROL PROBLEMS WITH CONSTRAINTS ON THE STATE // BSU Bulletin. Mathematics, Informatics. - 2019. №3. . - С. 42-59.
Title:
NONLOCAL DESCENT METHOD AT A SET OF ADMISSIBLE CONTROLS IN OPTIMAL CONTROL PROBLEMS WITH CONSTRAINTS ON THE STATE
Financing:
Работа выполнена при финансовой поддержке Министерства образования и науки РФ, проект 1.5049.2017/БЧ, и РФФИ, проект 18-41-030005-р-а.
Codes:
Annotation:
The article considers the method of constructing a relaxation sequence in the class of admissible controls in optimal control problems with constraints in the state. Re- laxation is carried out according to the functional of auxiliary extension problem and based on the construction of nonlocal conditions for improving control in the extension problem in the form of a fixed point problem. This form makes it possible to apply and modify the well-known apparatus of fixed-points theorem and methods for the search of improving admissible control. The construction of improving con- trols in the class of admissible controls allows us to apply the theory of extension for justification of sufficient conditions for constructing a minimizing sequence. The comparative effectiveness of the proposed descent method is illustrated by cal- culation of the well-known model problem.
Keywords:
controlled system; constraints on the state; conditions for improving control; fixed point problem; sufficient optimality conditions.
List of references:
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Samarskii A. A., Gulin A. V. Chislennye metody [Numerical Methods]. Mos- cow: Nauka Publ., 1989. 432 p.
Grachev N. I., Filkov A. N. Reshenie zadach optimalnogo upravleniya v sisteme DISO [Solution of Optimal Control Problems in DISO System]. Moscow: VTs AS USSR Computer Center, 1986. 66 p.
Tyatyushkin A. I. Mnogometodnaya tekhnologiya optimizatsii upravlyaemykh system [Multi-Method Technology for Optimizing Controlled Systems]. Novosibirsk: Nauka Publ., 2006. 343 p.
Bartenyev O. V. Fortran dlya professionalov. Matematicheskaya biblioteka IMSL [Fortran for Professionals. IMSL Mathematical Library]. Moscow: Dialog-MIFI Publ., 2001. Part 2. 320 p.
Fedorenko R. P. Priblizhennoe reshenie zadach optimalnogo upravleniya [An Approximate Solution to Optimal Control Problems]. Moscow: Nauka Publ., 1978. 488 p.
Gurman V. I. Printsip rasshireniya v zadachakh upravleniya [Extension Princi- ple in Control Problems]. Moscow: Nauka Publ., 1997. 288 p.
Vasilyev F. P. Chislennye metody resheniya ekstremalnykh zadach [Numerical Methods for Solving Extremum Problems]. Moscow: Nauka Publ., 1980. 518 p.
Vasilyev O. V. Lektsii po metodam optimizatsii [Lectures on Optimization Methods]. Irkutsk: Irkutsk State Univ. Publ., 1994. 340 p.
Srochko V. A. Iteratsionnye metody resheniya zadach optimalnogo upravleniya [Iterative Methods for Solving Optimal Control Problems]. Moscow: Fizmatlit Publ., 2000. 160 p.
Buldaev A. S. Metody vozmushchenii v zadachakh uluchsheniya i optimizatsii upravlyaemykh system [Perturbation Methods in Problems of Improving and Optimizing Controlled Systems]. Ulan-Ude: Buryat State Univ. Publ., 2008. 260 p.
Buldaev A. S., Khishektueva I.-Kh. The Fixed Point Method in Parametric Op- timization Problems for Systems. Automation and Remote Control. 2013. V. 74. No. 12. Pp.1927–1934.
Buldaev A. S. Metody nepodvizhnykh tochek na osnove operatsii proektiro- vaniya v zadachakh optimizatsii upravlyayushchikh funktsii i parametrov di- namicheskikh system [Fixed-Point Methods Based on Projection in Optimization Prob- lems of Control Functions and Parameters of Dynamic Systems]. Vestnik Buryatskogo gosuniversiteta. Matematika, informatika. 2017. No. 1. Pp. 38–54. DOI: 10.18101/2304-5728-2017-1-38-54.
Buldaev A. S., Burlakov I. D. About One Approach to Numerical Solution of Nonlinear Optimal Speed Problems. Bulletin of the South Ural State University. Series: Mathematical Modeling, Programming & Computer Software. 2018. V. 11. No. 4. Pp. 55–66. DOI: 10.14529/mmp180404.
Samarskii A. A., Gulin A. V. Chislennye metody [Numerical Methods]. Mos- cow: Nauka Publ., 1989. 432 p.
Grachev N. I., Filkov A. N. Reshenie zadach optimalnogo upravleniya v sisteme DISO [Solution of Optimal Control Problems in DISO System]. Moscow: VTs AS USSR Computer Center, 1986. 66 p.
Tyatyushkin A. I. Mnogometodnaya tekhnologiya optimizatsii upravlyaemykh system [Multi-Method Technology for Optimizing Controlled Systems]. Novosibirsk: Nauka Publ., 2006. 343 p.
Bartenyev O. V. Fortran dlya professionalov. Matematicheskaya biblioteka IMSL [Fortran for Professionals. IMSL Mathematical Library]. Moscow: Dialog-MIFI Publ., 2001. Part 2. 320 p.
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