On a system of Hamilton-Jacobi-Bellman inequalities associated to a minimax problem with additive final cost
We study a minimax optimal control problem with finite horizon and additive final cost. After introducing an auxiliary problem, we analyze the dynamical programming principle (DPP) and we present a Hamilton-Jacobi-Bellman (HJB) system. We prove the existence and uniqueness of a viscosity solution fo...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203302108 |
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| _version_ | 1832549899408769024 |
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| author | Silvia C. Di Marco Roberto L. V. González |
| author_facet | Silvia C. Di Marco Roberto L. V. González |
| author_sort | Silvia C. Di Marco |
| collection | DOAJ |
| description | We study a minimax optimal control problem with finite horizon
and additive final cost. After introducing an auxiliary problem,
we analyze the dynamical programming principle (DPP) and we
present a Hamilton-Jacobi-Bellman (HJB) system. We prove the
existence and uniqueness of a viscosity solution for this system.
This solution is the cost function of the auxiliary problem and
it is possible to get the solution of the original problem in
terms of this solution. |
| format | Article |
| id | doaj-art-f26de3b141de4e0ab3bdd342342f17a4 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-f26de3b141de4e0ab3bdd342342f17a42025-02-03T06:08:24ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-012003724517453810.1155/S0161171203302108On a system of Hamilton-Jacobi-Bellman inequalities associated to a minimax problem with additive final costSilvia C. Di Marco0Roberto L. V. González1CONICET, Instituto de Matematica Beppo Levi, FCEIA, Universidad Nacional de Rosario, Pellegrini 250, Rosario 2000, ArgentinaCONICET, Instituto de Matematica Beppo Levi, FCEIA, Universidad Nacional de Rosario, Pellegrini 250, Rosario 2000, ArgentinaWe study a minimax optimal control problem with finite horizon and additive final cost. After introducing an auxiliary problem, we analyze the dynamical programming principle (DPP) and we present a Hamilton-Jacobi-Bellman (HJB) system. We prove the existence and uniqueness of a viscosity solution for this system. This solution is the cost function of the auxiliary problem and it is possible to get the solution of the original problem in terms of this solution.http://dx.doi.org/10.1155/S0161171203302108 |
| spellingShingle | Silvia C. Di Marco Roberto L. V. González On a system of Hamilton-Jacobi-Bellman inequalities associated to a minimax problem with additive final cost International Journal of Mathematics and Mathematical Sciences |
| title | On a system of Hamilton-Jacobi-Bellman inequalities associated to a minimax problem with additive final cost |
| title_full | On a system of Hamilton-Jacobi-Bellman inequalities associated to a minimax problem with additive final cost |
| title_fullStr | On a system of Hamilton-Jacobi-Bellman inequalities associated to a minimax problem with additive final cost |
| title_full_unstemmed | On a system of Hamilton-Jacobi-Bellman inequalities associated to a minimax problem with additive final cost |
| title_short | On a system of Hamilton-Jacobi-Bellman inequalities associated to a minimax problem with additive final cost |
| title_sort | on a system of hamilton jacobi bellman inequalities associated to a minimax problem with additive final cost |
| url | http://dx.doi.org/10.1155/S0161171203302108 |
| work_keys_str_mv | AT silviacdimarco onasystemofhamiltonjacobibellmaninequalitiesassociatedtoaminimaxproblemwithadditivefinalcost AT robertolvgonzalez onasystemofhamiltonjacobibellmaninequalitiesassociatedtoaminimaxproblemwithadditivefinalcost |