Sufficiency for Weak Minima in Optimal Control Subject to Mixed Constraints

For optimal control problems of Bolza involving time-state-control mixed constraints, containing inequalities and equalities, fixed initial end-point, variable final end-point, and nonlinear dynamics, sufficient conditions for weak minima are derived. The proposed algorithm allows us to avoid hypoth...

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Bibliographic Details
Published inSymmetry (Basel) Vol. 14; no. 8; p. 1520
Main Author Licea, Gerardo Sánchez
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.08.2022
Subjects
Algorithms
free final end-point
Hypotheses
Inequality
Minima
mixed constraints
Nonlinear dynamics
Optimal control
Parameterization
sufficiency
weak minima
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Summary:For optimal control problems of Bolza involving time-state-control mixed constraints, containing inequalities and equalities, fixed initial end-point, variable final end-point, and nonlinear dynamics, sufficient conditions for weak minima are derived. The proposed algorithm allows us to avoid hypotheses such as the continuity of the second derivatives of the functions delimiting the problems, the continuity of the optimal controls or the parametrization of the final variable end-point. We also present a relaxation relative to some similar works, in the sense that we arrive essentially to the same conclusions but making weaker assumptions.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14081520