Fixed-Point Methods in Optimization Problems for Control Systems

In this paper, we consider a new approach to optimization of nonlinear control systems based on the representation of optimality conditions and improvement of the control in the form of special fixed-point problems for control operators. We propose algorithms for approximate solution of optimal cont...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 279; no. 5; pp. 594 - 606
Main Author Buldaev, A. S.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 23.03.2024
Springer
Springer Nature B.V
Subjects
Algorithms
Analysis
Control systems
Iterative methods
Mathematical optimization
Mathematics
Mathematics and Statistics
Methods
Nonlinear control
Nonlinear systems
Optimal control
Optimization
49Kxx
control system
numerical optimization algorithms
conditions for improvement and optimality of control
fixed-point problem
37Cxx
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ISSN1072-3374
1573-8795
DOI10.1007/s10958-024-07041-z

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Summary:In this paper, we consider a new approach to optimization of nonlinear control systems based on the representation of optimality conditions and improvement of the control in the form of special fixed-point problems for control operators. We propose algorithms for approximate solution of optimal control problems based on iterative methods for finding fixed points. The effectiveness of the optimization methods proposed is illustrated by model and test problems.
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ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-024-07041-z