BSU Bulletin. Mathematics, Informatics
Bibliographic description:
OPERATOR EQUATIONS AND MAXIMUM PRINCIPLE ALGORITHMS IN OPTIMAL CONTROL PROBLEMS // BSU Bulletin. Mathematics, Informatics. - 2020. №1. . - С. 35-53.
Title:
OPERATOR EQUATIONS AND MAXIMUM PRINCIPLE ALGORITHMS IN OPTIMAL CONTROL PROBLEMS
Financing:
Работа выполнена при финансовой поддержке РФФИ, проект 18-41-030005-р-а.
Codes:
Annotation:
The article deals with a new developing approach to the numerical solution of non- linear optimal control problems, based on the construction of operator equations in the form of fixed point problems characterizing optimal control conditions. This form makes it possible to apply and modify the well-known apparatus of the theory and methods of fixed points for searching of extremal controls. The proposed iterative algo- rithms of fixed points of the maximum principle have the nonlocality property of suc- cessive control approximations and the absence of a parametric search procedure for improving approximations at each iteration, which is characteristic of the well-known standard methods of the gradient maximum principle. We have considered the condi- tions for convergence of the constructed iterative processes based on the principle of contracting mappings.
Keywords:
controllable system; control statement; maximum principle; fixed point problem; iterative algorithm; convergence of the iterative process.
List of references:
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Samarskii A. A., Gulin A. V. Chislennye metody [Numerical Methods]. M.: Nauka Publ., 1989. 432 p.
Buldaev A. S. Metody vozmushchenii v zadachakh uluchsheniya i op-timizatsii upravlyaemykh system [Perturbation Methods in the Problems of Improving and Opti- mizing Controllable Systems]. Ulan-Ude: Buryat State Univ. Publ., 2008. 260 p.
Buldaev A. S. Metody nepodvizhnykh tochek printsipa maksimuma [Methods of Fixed Points of the Maximum Principle]. Vestnik Buryatskogo gosuniversiteta. Matematika, informatika. 2015. No. 4. P. 36–46.
Buldaev A. S. Zadachi i metody nepodvizhnykh tochek printsipa maksimuma [Problems and Methods of Fixed Points of the Maximum Principle]. Izvestiya Irkut- skogo gosudarstvennogo universiteta. Ser. Matematika. 2015. Vol. 14. Pp. 31–41.
Chernousko F. L. Otsenivanie fazovogo sostoyaniya dinamicheskikh system [Derivation of Estimate for the Phase State of Dynamical Systems]. Moscow: Nauka Publ., 1988. 320 p.
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