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Weak Measurable Optimal Controls for the Problems of Bolza

Author

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  • Gerardo Sánchez Licea

    (Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad de México 04510, Mexico)

Abstract

Two sufficiency theorems for parametric and a nonparametric problems of Bolza in optimal control are derived. The dynamics of the problems are nonlinear, the initial and final states are free, and the main results can be applied when nonlinear mixed time-state-control inequality and equality constraints are presented. The deviation between admissible costs and optimal costs around the optimal control is estimated by functionals playing the role of the square of some norms.

Suggested Citation

  • Gerardo Sánchez Licea, 2021. "Weak Measurable Optimal Controls for the Problems of Bolza," Mathematics, MDPI, vol. 9(2), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:2:p:191-:d:482954
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    References listed on IDEAS

    as
    1. Walter Alt & Ursula Felgenhauer & Martin Seydenschwanz, 2018. "Euler discretization for a class of nonlinear optimal control problems with control appearing linearly," Computational Optimization and Applications, Springer, vol. 69(3), pages 825-856, April.
    2. H. Maurer, 1999. "Sufficient conditions and sensitivity analysisfor economic control problems," Annals of Operations Research, Springer, vol. 88(0), pages 3-14, January.
    3. K. Malanowski & H. Maurer & S. Pickenhain, 2004. "Second-Order Sufficient Conditions for State-Constrained Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 123(3), pages 595-617, December.
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