Second order sufficient conditions of a linear optimal control problem

ARONNA, MARÍA SOLEDAD; BONNANS, J. FRÉDÉRIC; DMITRUK, ANDREI; LOTITO, PABLO ANDRÉS

Rosario

Congreso; Congreso de Matemática Aplicada, Computacional e Industrial; 2010

Asociación Argentina de Matemática Aplicada, Computacional e Industrial

In this work we present second order sufficient condition of an optimal control problem with singular arcs. We work on problems with scalar control, and a simple control constraint. These problems have been studied by Dmitruk [3], and Bonnans and Osmolovskii [1].  To obtain these conditions we use the Goh Transformation to introduce new variables and we arrive to necessary and sufficient conditions in these new variables. REFERENCES[1]  J.F. BONNANS AND N.P. OSMOLOVSKII, Second-order analysis of optimal control problems with control and initial-final state constraints, Rapport de recherche INRIA, RR-6707 (2008).[2]  A.V. DMITRUK, Quadratic order conditions for a Pontryagin minimum in an optimal control problem linear in the control in Math. USSR Izvestiya, 28 (1987), pp. 275-303.[3]  A.V. DMITRUK, Quadratic order conditions of a local minimum for singular extremals in a general optimal control problem, Proceedings of Symposia in Pure Mathematics, 64 (1999), pp. 163-198.