Weak Measurable Optimal Controls for the Problems of Bolza

Gerardo Sánchez Licea
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Gerardo Sánchez Licea: Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad de México 04510, Mexico

Mathematics, 2021, vol. 9, issue 2, 1-17

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.

Keywords: calculus of variations; optimal control; mixed restraints; inequality and equality restrictions; free initial and final states; sufficient conditions; weak minima; measurable optimal controls (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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