Second order sufficient conditions of a linear optimal control problem

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

Rosario

Congreso; II MACI 2009; 2009

ASAMACI - ARSIAM

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.