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Article Contents

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

• * Corresponding author: M. Soledad Aronna
This work was supported by the European Union under the 7th Framework Programme FP7-PEOPLE-2010-ITN Grant agreement number 264735-SADCO
• 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.

Mathematics Subject Classification: Primary: 49K15.

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