A NUMERICAL METHOD FOR SOLVING LINEAR–QUADRATIC CONTROL PROBLEMS WITH CONSTRAINTS
The paper is devoted to the optimal control problem for a linear system with integrally constrained control function. We study the problem of minimization of a linear terminal cost with terminal constraints given by a set of linear inequalities. For the solution of this problem we propose two-stage...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin.
2016-12-01
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/65 |
| _version_ | 1818358933553676288 |
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| author | Mikhail I. Gusev Igor V. Zykov |
| author_facet | Mikhail I. Gusev Igor V. Zykov |
| author_sort | Mikhail I. Gusev |
| collection | DOAJ |
| description | The paper is devoted to the optimal control problem for a linear system with integrally constrained control function. We study the problem of minimization of a linear terminal cost with terminal constraints given by a set of linear inequalities. For the solution of this problem we propose two-stage numerical algorithm, which is based on construction of the reachable set of the system. At the first stage we find a solution to finite–dimensional optimization problem with a linear objective function and linear and quadratic constraints. At the second stage we solve a standard linear–quadratic control problem, which admits a simple and effective solution. |
| first_indexed | 2024-12-13T20:36:52Z |
| format | Article |
| id | doaj.art-1d6ed1da59954bee921819203ec4bcb0 |
| institution | Directory Open Access Journal |
| issn | 2414-3952 |
| language | English |
| last_indexed | 2024-12-13T20:36:52Z |
| publishDate | 2016-12-01 |
| publisher | Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin. |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj.art-1d6ed1da59954bee921819203ec4bcb02022-12-21T23:32:15ZengKrasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin.Ural Mathematical Journal2414-39522016-12-012210.15826/umj.2016.2.00925A NUMERICAL METHOD FOR SOLVING LINEAR–QUADRATIC CONTROL PROBLEMS WITH CONSTRAINTSMikhail I. Gusev0Igor V. Zykov1Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, RussiaKrasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, RussiaThe paper is devoted to the optimal control problem for a linear system with integrally constrained control function. We study the problem of minimization of a linear terminal cost with terminal constraints given by a set of linear inequalities. For the solution of this problem we propose two-stage numerical algorithm, which is based on construction of the reachable set of the system. At the first stage we find a solution to finite–dimensional optimization problem with a linear objective function and linear and quadratic constraints. At the second stage we solve a standard linear–quadratic control problem, which admits a simple and effective solution.https://umjuran.ru/index.php/umj/article/view/65Optimal controlReachable setIntegral constraintsConvex programmingSemi-infinite linear programming. |
| spellingShingle | Mikhail I. Gusev Igor V. Zykov A NUMERICAL METHOD FOR SOLVING LINEAR–QUADRATIC CONTROL PROBLEMS WITH CONSTRAINTS Ural Mathematical Journal Optimal control Reachable set Integral constraints Convex programming Semi-infinite linear programming. |
| title | A NUMERICAL METHOD FOR SOLVING LINEAR–QUADRATIC CONTROL PROBLEMS WITH CONSTRAINTS |
| title_full | A NUMERICAL METHOD FOR SOLVING LINEAR–QUADRATIC CONTROL PROBLEMS WITH CONSTRAINTS |
| title_fullStr | A NUMERICAL METHOD FOR SOLVING LINEAR–QUADRATIC CONTROL PROBLEMS WITH CONSTRAINTS |
| title_full_unstemmed | A NUMERICAL METHOD FOR SOLVING LINEAR–QUADRATIC CONTROL PROBLEMS WITH CONSTRAINTS |
| title_short | A NUMERICAL METHOD FOR SOLVING LINEAR–QUADRATIC CONTROL PROBLEMS WITH CONSTRAINTS |
| title_sort | numerical method for solving linear quadratic control problems with constraints |
| topic | Optimal control Reachable set Integral constraints Convex programming Semi-infinite linear programming. |
| url | https://umjuran.ru/index.php/umj/article/view/65 |
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