Second order necessary and sufficient optimality conditions for singular solutions of partially-affine control problems

M. Soledad Aronna

doi:10.3934/dcdss.2018070

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2018, Volume 11, Issue 6: 1233-1258. Doi: 10.3934/dcdss.2018070

This issue Previous Article Recursive variational problems in nonreflexive Banach spaces with an infinite horizon: An existence result Next Article A study of structure-exploiting SQP algorithms for an optimal control problem with coupled hyperbolic and ordinary differential equation constraints

Second order necessary and sufficient optimality conditions for singular solutions of partially-affine control problems

M. Soledad Aronna^,

Escola de Matemática Aplicada, Fundação Getulio Vargas, Praia de Botafogo 190, 22250-900 Rio de Janeiro - RJ, Brazil

* Corresponding author: M. Soledad Aronna
* Corresponding author: M. Soledad Aronna

Received: March 2017

Revised: June 2017

Published: December 2018

This work was supported by the European Union under the 7th Framework Programme FP7-PEOPLE-2010-ITN Grant agreement number 264735-SADCO

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Abstract

In this article we study optimal control problems for systems that are affine with respect to some of the control variables and nonlinear in relation to the others. We consider finitely many equality and inequality constraints on the initial and final values of the state. We investigate singular optimal solutions for this class of problems, for which we obtain second order necessary and sufficient conditions for weak optimality in integral form. We also derive Goh pointwise necessary optimality conditions. We show an example to illustrate the results.

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Mathematics Subject Classification: Primary: 49K15.

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