The paper is a first step in proving second order sufficient optimality conditions for singular extremals. The conditions include regularity conditions on the Hamiltonian associated to the problem and the absence of conjugate times. The definition of conjugate time is given by means of a suitable linear Hamiltonian system. In a forthcoming paper it is proved that the linear Hamiltonian system is the one associated to the second variation of the problem.
ON SUFFICIENT OPTIMALITY CONDITIONS FOR A SINGULAR EXTREMAL / G. STEFANI. - ELETTRONICO. - IEEEcatalog number 03CH37475C:(2003), pp. 135-140. (Intervento presentato al convegno 43RD IEEE CONFERENCE ON DECISION AND CONTROL tenutosi a MAWI nel Dicembre) [10.1109/CDC.2003.1273039].
ON SUFFICIENT OPTIMALITY CONDITIONS FOR A SINGULAR EXTREMAL
STEFANI, GIANNA
2003
Abstract
The paper is a first step in proving second order sufficient optimality conditions for singular extremals. The conditions include regularity conditions on the Hamiltonian associated to the problem and the absence of conjugate times. The definition of conjugate time is given by means of a suitable linear Hamiltonian system. In a forthcoming paper it is proved that the linear Hamiltonian system is the one associated to the second variation of the problem.
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