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Normality, Controllability and Properness in Optimal Control

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Abstract

In this paper we show that, for optimal control problems involving equality and inequality constraints on the control function, the notions of normality and properness (or the Mangasarian–Fromovitz constraint qualification) of a trajectory relative to the set of constraints are equivalent. This is in contrast with some differences recently obtained between the theories of mathematical programming and optimal control, and it provides an important insight in the derivation of first and second order necessary optimality conditions for infinite dimensional problems.

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Acknowledgements

The first author is grateful to CONACYT for the financial support. The second author is grateful to DGAPA, from Universidad Nacional Autónoma de México, for the support given as part of the PASPA program during a sabbatical stay at the Department of Mathematical Sciences, University of Bath, United Kingdom.

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Authors and Affiliations

  1. SYSTEC - Departamento de Engenharia Electrotécnica e Computadores, Faculdade de Engenharia da Universidade do Porto, Rua Dr Roberto Frias s/n, 4200-465, Porto, Portugal

    Karla L. Cortez

  2. IIMAS, Universidad Nacional Autónoma de México, Apartado Postal 20-126, 01000, Mexico, Mexico

    Javier F. Rosenblueth

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  1. Karla L. Cortez
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  2. Javier F. Rosenblueth
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Correspondence to Javier F. Rosenblueth.

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Cortez, K.L., Rosenblueth, J.F. Normality, Controllability and Properness in Optimal Control. Appl Math Optim 84 (Suppl 1), 159–173 (2021). https://doi.org/10.1007/s00245-021-09765-9

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