Journal of Optimization Theory and Applications

, Volume 180, Issue 1, pp 235–255 | Cite as

On a Few Questions Regarding the Study of State-Constrained Problems in Optimal Control

  • Dmitry KaramzinEmail author
  • Fernando Lobo Pereira


The article is focused on the investigation of the necessary optimality conditions in the form of Pontryagin’s maximum principle for optimal control problems with state constraints. A number of results on this topic, which refine the existing ones, are presented. These results concern the nondegenerate maximum principle under weakened controllability assumptions and also the continuity of the measure Lagrange multiplier.


Optimal control Maximum principle State constraints 

Mathematics Subject Classification




We kindly thank professor A.V. Arutyunov for useful comments and fruitful discussions. The support from the Russian Foundation for Basic Research during the projects 16-31-60005, 18-29-03061, and the support of FCT R&D Unit SYSTEC—POCI-01-0145-FEDER-006933/SYSTEC funded by ERDF | COMPETE2020 | FCT/MEC | PT2020 extension to 2018, Project STRIDE NORTE-01-0145-FEDER-000033 funded by ERDF | NORTE2020, and FCT Project POCI-01-01-0145-FEDER-032485 funded by ERDF | COMPETE2020 | POCI are also acknowledged.


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Authors and Affiliations

  1. 1.Federal Research Center “Computer Science and Control” of the Russian Academy of SciencesMoscowRussia
  2. 2.University of PortoPortoPortugal

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