Strong and weak measurable optimal controls

Gerardo Sánchez Licea; Gerardo Sánchez Licea

doi:10.3934/math.2021291

AIMS Mathematics

2021, Volume 6, Issue 5: 4958-4978. doi: 10.3934/math.2021291

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Strong and weak measurable optimal controls

Gerardo Sánchez Licea ^,

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

Received: 11 November 2020 Accepted: 24 February 2021 Published: 03 March 2021
MSC : 49K15

Sufficient conditions for weak and strong minima in an optimal control problem of Lagrange are provided. This sufficiency theory is applicable for problems containing fixed end-points, nonlinear dynamics, nonlinear isoperimetric inequality and equality constraints together with nonlinear mixed time-state-control pointwise inequality and equality restrictions. The presence of purely measurable optimal controls is a fundamental component of this theory.
- calculus of variations,
- optimal control,
- inequality and equality constraints,
- sufficiency,
- strong minima,
- weak minima,
- measurable optimal controls
Citation: Gerardo Sánchez Licea. Strong and weak measurable optimal controls[J]. AIMS Mathematics, 2021, 6(5): 4958-4978. doi: 10.3934/math.2021291

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Abstract

Sufficient conditions for weak and strong minima in an optimal control problem of Lagrange are provided. This sufficiency theory is applicable for problems containing fixed end-points, nonlinear dynamics, nonlinear isoperimetric inequality and equality constraints together with nonlinear mixed time-state-control pointwise inequality and equality restrictions. The presence of purely measurable optimal controls is a fundamental component of this theory.

References

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