Necessary conditions for a weak minimumin optimal control problems with integral equationson a variable time interval

Andrei V. Dmitruk; Nikolai P. Osmolovskii

doi:10.3934/dcds.2015.35.4323

Article Contents

2015, Volume 35, Issue 9: 4323-4343. Doi: 10.3934/dcds.2015.35.4323

This issue Previous Article Higher order discrete controllability and the approximation of the minimum time function Next Article Integral representations for bracket-generating multi-flows

Necessary conditions for a weak minimum in optimal control problems with integral equations on a variable time interval

Andrei V. Dmitruk^1, and
Nikolai P. Osmolovskii^2,

1.
Russian Academy of Sciences, Central Economics and Mathematics Institute and Lomonosov Moscow State University, Russia 117418, Moscow, Nakhimovskii prospekt, 47
2.
Systems Research Institute, Polish Academy of Sciences, Warszawa, Moscow State University of Civil Engineering

Received: April 2014

Revised: October 2014

Published: May 2017

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Abstract

We study an optimal control problem with Volterra-type integral equation, considered on a nonfixed time interval, subject to endpoint constraints of equality and inequality type. We obtain first-order necessary optimality conditions for an extended weak minimum, the notion of which is a natural generalization of the notion of weak minimum with account of variations of the time. The conditions obtained generalize the Euler--Lagrange equation and transversality conditions for the Lagrange problem in the classical calculus of variations with ordinary differential equations.

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Mathematics Subject Classification: Primary: 49K21; Secondary: 49K15, 90C30.

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