Quadratic order conditions for an extended weak minimum inoptimal control problems with intermediate and mixed constraints

Andrei V. Dmitruk; Alexander M. Kaganovich

doi:10.3934/dcds.2011.29.523

Article Contents

2011, Volume 29, Issue 2: 523-545. Doi: 10.3934/dcds.2011.29.523

This issue Previous Article Nirenberg's contributions to complex analysis Next Article Decay estimation for positive solutions of a $\gamma$-Laplace equation

Quadratic order conditions for an extended weak minimum in optimal control problems with intermediate and mixed constraints

Andrei V. Dmitruk^1, and
Alexander M. Kaganovich^2,

1.
Central Economics and Mathematics Institute of the Russian Academy of Sciences, Nakhimovskii prospekt, 47, Moscow 117418
2.
Moscow State University, Faculty of Computational Mathematics and Cybernetics, GSP-2, Leninskie Gory, VMK MGU, Moscow 119992

Received: July 31, 2009

Revised: March 31, 2010

Published: May 2011

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Abstract

We consider a general optimal control problem with intermediate and mixed constraints. Using a natural transformation (replication of the state and control variables), this problem is reduced to a standard optimal control problem with mixed constraints, which makes it possible to obtain quadratic order conditions for an "extended" weak minimum. The conditions obtained are applied to the problem of light refraction.

Keywords:

Intermediate constraints,
mixed constraints,
weak minimum,
Euler--Lagrange equation,
second variation,
replication of state and control variables.

Mathematics Subject Classification: Primary: 49K15; Secondary: 93B12.

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References

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