Relationship Between the Maximum Principle and Dynamic Programming for Minimax Problems
This paper is concerned with the relationship between the maximum principle and dynamic programming for a large class of optimal control problems with maximum running cost. Inspired by a technique introduced by Vinter in the 1980s, we are able to obtain jointly a global and a partial sensitivity rel...
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| Veröffentlicht in: | Applied mathematics & optimization 2023-04, Vol.87 (2), p.34, Article 34 |
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| creator | Hermosilla, Cristopher Zidani, Hasnaa |
| description | This paper is concerned with the relationship between the maximum principle and dynamic programming for a large class of optimal control problems with maximum running cost. Inspired by a technique introduced by Vinter in the 1980s, we are able to obtain jointly a global and a partial sensitivity relation that link the coextremal with the value function of the problem at hand. One of the main contributions of this work is that these relations are derived by using a single perturbed problem, and therefore, both sensitivity relations hold, at the same time, for the same coextremal. As a by-product, and thanks to the level-set approach, we obtain a new set of sensitivity relations for Mayer problems with state constraints. One important feature of this last result is that it holds under mild assumptions, without the need of imposing strong compatibility assumptions between the dynamics and the state constraints set. |
| doi_str_mv | 10.1007/s00245-022-09943-3 |
| format | Article |
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| subjects | Applied mathematics Calculus of Variations and Optimal Control Optimization Control Dynamic programming Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Maximum principle Minimax technique Numerical and Computational Physics Optimal control Optimization Ordinary differential equations Sensitivity Simulation Systems Theory Theoretical |
| title | Relationship Between the Maximum Principle and Dynamic Programming for Minimax Problems |
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