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Open AccessArticle

Sufficiency for Purely Essentially Bounded Optimal Controls

Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad de Mexico 04510, Mexico
Symmetry 2020, 12(2), 238; https://doi.org/10.3390/sym12020238
Received: 13 December 2019 / Revised: 10 January 2020 / Accepted: 17 January 2020 / Published: 4 February 2020
(This article belongs to the Special Issue Advance in Nonlinear Analysis and Optimization)
For optimal control problems of Bolza with variable and free end-points, nonlinear dynamics, nonlinear isoperimetric inequality and equality restrictions, and nonlinear pointwise mixed time-state-control inequality and equality constraints, sufficient conditions for strong minima are derived. The algorithm used to prove the main theorem of the paper includes a crucial symmetric inequality, making this technique an independent self-contained method of classical concepts such as embedding theorems from ordinary differential equations, Mayer fields, Riccati equations, or Hamilton–Jacobi theory. Moreover, the sufficiency theory given in this article is able to detect discontinuous solutions, that is, solutions which need to be neither continuous nor piecewise continuous but only essentially bounded. View Full-Text
Keywords: calculus of variations; optimal control; symmetric inequalities; isoperimetric and mixed constraints; inequality and equality constraints; free end-points; sufficiency; strong minima; purely essentially bounded optimal controls calculus of variations; optimal control; symmetric inequalities; isoperimetric and mixed constraints; inequality and equality constraints; free end-points; sufficiency; strong minima; purely essentially bounded optimal controls
MDPI and ACS Style

Sánchez Licea, G. Sufficiency for Purely Essentially Bounded Optimal Controls. Symmetry 2020, 12, 238.

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