Volume 27, 2021
|Number of page(s)||24|
|Published online||12 July 2021|
Necessary optimality conditions for minimax optimal control problems with mixed constraints
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; email@example.com
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
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