| Issue |
ESAIM: COCV
Volume 27, 2021
|
|
|---|---|---|
| Article Number | 72 | |
| Number of page(s) | 24 | |
| DOI | https://doi.org/10.1051/cocv/2021069 | |
| Published online | 12 July 2021 | |
Necessary optimality conditions for minimax optimal control problems with mixed constraints
1
Universidad Mayor de San Andrés, Carrera de Matemática,
La Paz, Bolivia.
2
Universidade do Porto, Faculdade de Engenharia, DEEC, Systec,
Porto, Portugal.
3
Departamento de Matemática, Instituto de Biociências, Letras e Ciências Exatas, UNESP - Universidade Estadual Paulista,
São José do Rio Preto,
SP, Brazil.
* Corresponding author; geraldo.silva@unesp.br
Received:
16
July
2020
Accepted:
22
June
2021
A weak maximal principle for minimax optimal control problems with mixed state-control equality and inequality constraints is provided. In the formulation of the minimax control problem we allow for parameter uncertainties in all functions involved: in the cost function, in the dynamical control system and in the equality and inequality constraints. Then a new constraint qualification of Mangassarian-Fromovitz type is introduced which allowed us to prove the necessary conditions of optimality. We also derived the optimality conditions under a full rank conditions type and showed that it is, as usual, a particular case of the Mangassarian-Fromovitz type condition case. Illustrative examples are presented.
Mathematics Subject Classification: 49J35 / 49J15 / 49J21
Key words: Minimax optimal control problems / mixed constrained / maximum principle / nonsmooth analysis
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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