Numerical approximation of constrained optimal control problems in delayed systems using an enhanced Rayleigh-Ritz algorithm.
Saved in:
| Title: | Numerical approximation of constrained optimal control problems in delayed systems using an enhanced Rayleigh-Ritz algorithm. |
|---|---|
| Authors: | Kafash, Behzad1 (AUTHOR) bkafash@ardakan.ac.ir |
| Source: | Applied Numerical Mathematics. Feb2026, Vol. 220, p104-122. 19p. |
| Subjects: | Rayleigh-Ritz method, Constrained optimization, Empirical research, Optimal control theory, Time delay systems, Approximation algorithms, Chebyshev polynomials, Mathematical optimization |
| Abstract: | • A modified Rayleigh-Ritz method based on shifted Chebyshev polynomials is proposed for optimal control problems governed by time delay systems, with or without constraints on the control and state variables. • The method transforms the constrained time-delay optimal control problem into a constrained optimization problem and guarantees convergence analytically. • The efficiency and robustness of the proposed scheme are demonstrated through multiple case studies, including the single-input/single-output system with control and final state constraint and the harmonic oscillator under various constraint scenarios. [Display omitted] In this study, a modified Rayleigh-Ritz method is presented for the solution of optimal control problems governed by time-delayed dynamical systems, considering both constrained and unconstrained control and state variables. In this approach, the control or state variables are approximated using shifted Chebyshev polynomials with unknown coefficients. The proposed modified Rayleigh-Ritz method transforms the constrained optimal control problems governed by time-delayed dynamical systems into an optimization problem with constraints. Furthermore, a computational algorithm is developed for implementing the proposed method, and its convergence is proven analytically. To evaluate the efficiency and accuracy of the proposed algorithm, several numerical examples are presented. These include the single-input/single-output system as a case study with control and final state constraints, and an optimal control problem of the harmonic oscillator under different scenarios, which involve constraints on state and control variables. [ABSTRACT FROM AUTHOR] |
| Copyright of Applied Numerical Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 189755534 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Numerical approximation of constrained optimal control problems in delayed systems using an enhanced Rayleigh-Ritz algorithm. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Kafash%2C+Behzad%22">Kafash, Behzad</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> bkafash@ardakan.ac.ir</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Applied+Numerical+Mathematics%22">Applied Numerical Mathematics</searchLink>. Feb2026, Vol. 220, p104-122. 19p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Rayleigh-Ritz+method%22">Rayleigh-Ritz method</searchLink><br /><searchLink fieldCode="DE" term="%22Constrained+optimization%22">Constrained optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Empirical+research%22">Empirical research</searchLink><br /><searchLink fieldCode="DE" term="%22Optimal+control+theory%22">Optimal control theory</searchLink><br /><searchLink fieldCode="DE" term="%22Time+delay+systems%22">Time delay systems</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+algorithms%22">Approximation algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Chebyshev+polynomials%22">Chebyshev polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: • A modified Rayleigh-Ritz method based on shifted Chebyshev polynomials is proposed for optimal control problems governed by time delay systems, with or without constraints on the control and state variables. • The method transforms the constrained time-delay optimal control problem into a constrained optimization problem and guarantees convergence analytically. • The efficiency and robustness of the proposed scheme are demonstrated through multiple case studies, including the single-input/single-output system with control and final state constraint and the harmonic oscillator under various constraint scenarios. [Display omitted] In this study, a modified Rayleigh-Ritz method is presented for the solution of optimal control problems governed by time-delayed dynamical systems, considering both constrained and unconstrained control and state variables. In this approach, the control or state variables are approximated using shifted Chebyshev polynomials with unknown coefficients. The proposed modified Rayleigh-Ritz method transforms the constrained optimal control problems governed by time-delayed dynamical systems into an optimization problem with constraints. Furthermore, a computational algorithm is developed for implementing the proposed method, and its convergence is proven analytically. To evaluate the efficiency and accuracy of the proposed algorithm, several numerical examples are presented. These include the single-input/single-output system as a case study with control and final state constraints, and an optimal control problem of the harmonic oscillator under different scenarios, which involve constraints on state and control variables. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Applied Numerical Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=189755534 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.apnum.2025.10.004 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 19 StartPage: 104 Subjects: – SubjectFull: Rayleigh-Ritz method Type: general – SubjectFull: Constrained optimization Type: general – SubjectFull: Empirical research Type: general – SubjectFull: Optimal control theory Type: general – SubjectFull: Time delay systems Type: general – SubjectFull: Approximation algorithms Type: general – SubjectFull: Chebyshev polynomials Type: general – SubjectFull: Mathematical optimization Type: general Titles: – TitleFull: Numerical approximation of constrained optimal control problems in delayed systems using an enhanced Rayleigh-Ritz algorithm. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Kafash, Behzad IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 02 Text: Feb2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 01689274 Numbering: – Type: volume Value: 220 Titles: – TitleFull: Applied Numerical Mathematics Type: main |
| ResultId | 1 |
