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Optimality Conditions (in Pontryagin Form)

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Optimal Control: Novel Directions and Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2180))

Abstract

This chapter aims at being a friendly presentation of various results related to optimality conditions of Optimal Control problems. Different classes of systems are considered, such as equations with time delays and/or state constraints, dynamics affine with respect to the control variables, problems governed by partial differential equations and systems arising from Classical Mechanics, among others.

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Notes

  1. 1.

    A function is semiconcave if it can be written as a sum of a concave function and a C 2 function.

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Authors and Affiliations

  1. Escola de Matemática Aplicada, Fundação Getúlio Vargas, Rio de Janeiro, Brazil

    Maria Soledad Aronna

  2. CEREMADE, UMR CNRS 7534, Université Paris Dauphine, PSL Research University, Paris, France

    Daniela Tonon

  3. Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    Andrea Boccia

  4. Escuela de Ciencias Matemáticas y Tecnología Informática, Yachay Tech, Urcuqui, Ecuador

    Cédric Martínez Campos

  5. Instituto de Matemáticas, Universidad de Valladolid, Valladolid, Spain

    Cédric Martínez Campos

  6. CNRS, IMJ-PRG, UMR 7586, Sorbonne Universités, UPMC, Paris, France

    Marco Mazzola

  7. Department of Natural Sciences, Hong Duc University, Thanh Hoa, Vietnam

    Luong Van Nguyen

  8. Mathematics Department, Penn State University, University Park, State College, PA, USA

    Michele Palladino

  9. Department of Statistics and Operation Research, University of Vienna, Vienna, Austria

    Teresa Scarinci

  10. XLIM-DMI, UMR CNRS 7252, Faculté des Sciences et Techniques, Université de Limoges, Limoges, France

    Francisco J. Silva

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  1. Maria Soledad Aronna
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  2. Daniela Tonon
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  4. Cédric Martínez Campos
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  5. Marco Mazzola
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  6. Luong Van Nguyen
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  7. Michele Palladino
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  8. Teresa Scarinci
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  9. Francisco J. Silva
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Correspondence to Maria Soledad Aronna .

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Editors and Affiliations

  1. CEREMADE, UMR CNRS 7534, Université Paris Dauphine, PSL Research University, Paris, France

    Daniela Tonon

  2. Escola de Matemática Aplicada, Fundação Getúlio Vargas, Rio de Janeiro, Brazil

    Maria Soledad Aronna

  3. Department of Mathematics, Imperial College London, London, United Kingdom

    Dante Kalise

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Aronna, M.S. et al. (2017). Optimality Conditions (in Pontryagin Form). In: Tonon, D., Aronna, M., Kalise, D. (eds) Optimal Control: Novel Directions and Applications. Lecture Notes in Mathematics, vol 2180. Springer, Cham. https://doi.org/10.1007/978-3-319-60771-9_1

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