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Essential Boundedness and Singularity in Optimal Control

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Abstract

Sufficient optimality conditions for optimal control problems involving isoperimetric and mixed inequality and equality constraints are derived. The main novelty of our approach is the fact that, for such problems, discontinuous and singular solutions can be detected. In other words, our result can deal with solutions for which the proposed optimal control is not continuous, but only essentially bounded, and the classical, crucial strengthened Legendre-Clebsch condition is no longer imposed.

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Funding

The authors are grateful to Dirección General de Asuntos del Personal Académico, from Universidad Nacional Autónoma de México, for the support given. The first author as part of the PASPA program during a sabbatical stay at the Department of Mathematical Sciences, University of Bath, UK, and the second author for the project PAPIIT-IN113318.

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Authors and Affiliations

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

    Javier F. Rosenblueth

  2. Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, 04510, Mexico City, Mexico

    Gerardo Sánchez Licea

Authors
  1. Javier F. Rosenblueth
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  2. Gerardo Sánchez Licea
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Correspondence to Javier F. Rosenblueth.

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Rosenblueth, J.F., Licea, G.S. Essential Boundedness and Singularity in Optimal Control. J Dyn Control Syst 27, 87–105 (2021). https://doi.org/10.1007/s10883-020-09482-6

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  • DOI: https://doi.org/10.1007/s10883-020-09482-6

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