A boundary value problem for a non-linear difference equation
A boundary value problem for a non-linear difference equation of order three is considered. We show that this equation can be interpreted as the equation satisfied by the value function in a stochastic optimal control problem. We thus obtain an expression for the solution of the non-linear differenc...
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| Format: | Article |
| Language: | English |
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Polish Academy of Sciences
2024-01-01
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| Series: | Archives of Control Sciences |
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| Online Access: | https://journals.pan.pl/Content/130019/art06_int.pdf |
| _version_ | 1797354018760032256 |
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| author | Mario Lefebvre |
| author_facet | Mario Lefebvre |
| author_sort | Mario Lefebvre |
| collection | DOAJ |
| description | A boundary value problem for a non-linear difference equation of order three is considered. We show that this equation can be interpreted as the equation satisfied by the value function in a stochastic optimal control problem. We thus obtain an expression for the solution of the non-linear difference equation that can be used to find an explicit solution to this equation. An example is presented. |
| first_indexed | 2024-03-08T13:39:17Z |
| format | Article |
| id | doaj.art-75fc538f9659412bb3fd4281a20bb0ec |
| institution | Directory Open Access Journal |
| issn | 1230-2384 |
| language | English |
| last_indexed | 2024-03-08T13:39:17Z |
| publishDate | 2024-01-01 |
| publisher | Polish Academy of Sciences |
| record_format | Article |
| series | Archives of Control Sciences |
| spelling | doaj.art-75fc538f9659412bb3fd4281a20bb0ec2024-01-16T12:00:44ZengPolish Academy of SciencesArchives of Control Sciences1230-23842024-01-01vol. 33No 4829837https://doi.org/10.24425/acs.2023.148883A boundary value problem for a non-linear difference equationMario Lefebvre0Department of Mathematics and Industrial Engineering,Polytechnique Montréal, C.P. 6079, Succursale Centreville, Montréal, Canada H3C 3A7, CanadaA boundary value problem for a non-linear difference equation of order three is considered. We show that this equation can be interpreted as the equation satisfied by the value function in a stochastic optimal control problem. We thus obtain an expression for the solution of the non-linear difference equation that can be used to find an explicit solution to this equation. An example is presented.https://journals.pan.pl/Content/130019/art06_int.pdfhigher-order difference equationsoptimal controldynamic programmingfirst-passage timehoming problem |
| spellingShingle | Mario Lefebvre A boundary value problem for a non-linear difference equation Archives of Control Sciences higher-order difference equations optimal control dynamic programming first-passage time homing problem |
| title | A boundary value problem for a non-linear difference equation |
| title_full | A boundary value problem for a non-linear difference equation |
| title_fullStr | A boundary value problem for a non-linear difference equation |
| title_full_unstemmed | A boundary value problem for a non-linear difference equation |
| title_short | A boundary value problem for a non-linear difference equation |
| title_sort | boundary value problem for a non linear difference equation |
| topic | higher-order difference equations optimal control dynamic programming first-passage time homing problem |
| url | https://journals.pan.pl/Content/130019/art06_int.pdf |
| work_keys_str_mv | AT mariolefebvre aboundaryvalueproblemforanonlineardifferenceequation AT mariolefebvre boundaryvalueproblemforanonlineardifferenceequation |