BSU Bulletin. Mathematics, Informatics
Bibliographic description:
, ON ONE APPROACH TO OPTIMIZATION OF THE CONTROLLED SYSTEMS WITH RESTRICTIONS ON THE BASIS OF A FIXED POINT PROBLEM // BSU Bulletin. Mathematics, Informatics. - 2018. №2. . - С. 29-41.
Title:
ON ONE APPROACH TO OPTIMIZATION OF THE CONTROLLED SYSTEMS WITH RESTRICTIONS ON THE BASIS OF A FIXED POINT PROBLEM
Financing:
Codes:
Annotation:
In the article we consider a new approach to solving optimal control problems with constraints based on construction and solution of a system of conditions for improv- ing control in the form of a fixed point problem for control operator. To construct these conditions we apply the transition to an auxiliary problem without restrictions and with a regular Lagrange functional. Iterative algorithms for successive control improvement are constructed on the basis of a fixed point problem. We illustrate this approach by an example.
Keywords:
controlled system with constraints; conditions for improving control; a fixed point problem.
List of references:
Alekseev V. M., Tikhomirov V. M., Fomin S. V. Optimal'noe upravlenie [Op- timal Control]. Moscow: Nauka Publ., 1979. 428 p.
Afanasiev A. P., Dikusar V. V., Milyutin A. A., Chukanov S. A. Neobkhodimoe uslovie v optimal'nom upravlenii [Necessary Condition in Optimal Control]. Moscow: Nauka Publ., 1990. 320 p.
Srochko V. A. Iteratsionnye metody resheniya zadach optimal'nogo 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 sistem [Perturbation Methods in Problems of Improving and Optimiz- ing Control Systems]. Ulan-Ude: Buryat State University Publ, 2008. 260 p.
Buldaev A. S. Metody nepodvizhnykh tochek na osnove operatsii proektiro- vaniya v zadachakh optimizatsii upravlyayushchikh funktsii i parametrov di- namicheskikh sistem [Fixed-Point Methods Based on Design Operations in Optimiza- tion Problems of Control Functions and Parameters of Dynamical Systems]. Vestnik Buryatskogo gosuniversiteta. Matematika, informatika — Bulletin of Buryat State Uni- versity. Mathematics, Computer Science. 2017. No. 1. Pp. 38–54. DOI: 10.18101/2304- 5728-2017-1-38-54.
Samarskii A. A., Gulin A. V. Chislennye metody [Numerical Methods]. Mos- cow: Nauka Publ., 1989. 432 p.
Gurman V. I. Printsip rasshireniya v zadachakh upravleniya [Expansion Princi- ple in Control Problems]. Moscow: Nauka Publ., 1997. 288 p.
Afanasiev A. P., Dikusar V. V., Milyutin A. A., Chukanov S. A. Neobkhodimoe uslovie v optimal'nom upravlenii [Necessary Condition in Optimal Control]. Moscow: Nauka Publ., 1990. 320 p.
Srochko V. A. Iteratsionnye metody resheniya zadach optimal'nogo 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 sistem [Perturbation Methods in Problems of Improving and Optimiz- ing Control Systems]. Ulan-Ude: Buryat State University Publ, 2008. 260 p.
Buldaev A. S. Metody nepodvizhnykh tochek na osnove operatsii proektiro- vaniya v zadachakh optimizatsii upravlyayushchikh funktsii i parametrov di- namicheskikh sistem [Fixed-Point Methods Based on Design Operations in Optimiza- tion Problems of Control Functions and Parameters of Dynamical Systems]. Vestnik Buryatskogo gosuniversiteta. Matematika, informatika — Bulletin of Buryat State Uni- versity. Mathematics, Computer Science. 2017. No. 1. Pp. 38–54. DOI: 10.18101/2304- 5728-2017-1-38-54.
Samarskii A. A., Gulin A. V. Chislennye metody [Numerical Methods]. Mos- cow: Nauka Publ., 1989. 432 p.
Gurman V. I. Printsip rasshireniya v zadachakh upravleniya [Expansion Princi- ple in Control Problems]. Moscow: Nauka Publ., 1997. 288 p.
Article.pdf