The Meaning and Accuracy of the Improving Functions in the Solution of the CBQR by Krotov’s Method
A new solution to the continuous-time bilinear quadratic regulator optimal control problem (CBQR) was recently developed using Krotov’s Method. This paper provides two theoretical results related to the properties of that solution. The first discusses the equivalent representation of the cost-to-go...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-02-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/12/4/611 |
| _version_ | 1797297528441405440 |
|---|---|
| author | Ido Halperin |
| author_facet | Ido Halperin |
| author_sort | Ido Halperin |
| collection | DOAJ |
| description | A new solution to the continuous-time bilinear quadratic regulator optimal control problem (CBQR) was recently developed using Krotov’s Method. This paper provides two theoretical results related to the properties of that solution. The first discusses the equivalent representation of the cost-to-go performance index. The second one breaks down this equivalence into smaller identities referencing the components of the performance index. The paper shows how these results can be used to verify the numerical accuracy of the computed solution. Additionally, the meaning of the improving function and the equivalent representation, which are the main elements in the discussed CBQR’s solution, are explained according to the derived notions. A numerical example of structural control application exemplifies the significance of these results and how they can be applied to a specific CBQR problem. |
| first_indexed | 2024-03-07T22:22:37Z |
| format | Article |
| id | doaj.art-333042e5546648d495a06046d5fab3b9 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-07T22:22:37Z |
| publishDate | 2024-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-333042e5546648d495a06046d5fab3b92024-02-23T15:26:17ZengMDPI AGMathematics2227-73902024-02-0112461110.3390/math12040611The Meaning and Accuracy of the Improving Functions in the Solution of the CBQR by Krotov’s MethodIdo Halperin0The Department of Civil Engineering, Ariel University, Ariel 40700, IsraelA new solution to the continuous-time bilinear quadratic regulator optimal control problem (CBQR) was recently developed using Krotov’s Method. This paper provides two theoretical results related to the properties of that solution. The first discusses the equivalent representation of the cost-to-go performance index. The second one breaks down this equivalence into smaller identities referencing the components of the performance index. The paper shows how these results can be used to verify the numerical accuracy of the computed solution. Additionally, the meaning of the improving function and the equivalent representation, which are the main elements in the discussed CBQR’s solution, are explained according to the derived notions. A numerical example of structural control application exemplifies the significance of these results and how they can be applied to a specific CBQR problem.https://www.mdpi.com/2227-7390/12/4/611optimal controlKrotov’s methodnumerical accuracyimproving functionequivalent representation |
| spellingShingle | Ido Halperin The Meaning and Accuracy of the Improving Functions in the Solution of the CBQR by Krotov’s Method Mathematics optimal control Krotov’s method numerical accuracy improving function equivalent representation |
| title | The Meaning and Accuracy of the Improving Functions in the Solution of the CBQR by Krotov’s Method |
| title_full | The Meaning and Accuracy of the Improving Functions in the Solution of the CBQR by Krotov’s Method |
| title_fullStr | The Meaning and Accuracy of the Improving Functions in the Solution of the CBQR by Krotov’s Method |
| title_full_unstemmed | The Meaning and Accuracy of the Improving Functions in the Solution of the CBQR by Krotov’s Method |
| title_short | The Meaning and Accuracy of the Improving Functions in the Solution of the CBQR by Krotov’s Method |
| title_sort | meaning and accuracy of the improving functions in the solution of the cbqr by krotov s method |
| topic | optimal control Krotov’s method numerical accuracy improving function equivalent representation |
| url | https://www.mdpi.com/2227-7390/12/4/611 |
| work_keys_str_mv | AT idohalperin themeaningandaccuracyoftheimprovingfunctionsinthesolutionofthecbqrbykrotovsmethod AT idohalperin meaningandaccuracyoftheimprovingfunctionsinthesolutionofthecbqrbykrotovsmethod |