For an optimal control problem we define a second variation which is invariant under change of coordinates, and realize it as a linear-quadratic problem. When the strong Legendre condition is satisfied we give a complete Hamiltonian characterization of the index and of the nullity of the second variation.
An invariant second variation in optimal control / A. AGRACHEV ; G. STEFANI ; P. ZEZZA. - In: INTERNATIONAL JOURNAL OF CONTROL. - ISSN 0020-7179. - STAMPA. - 71:(1998), pp. 689-715. [10.1080/002071798221533]
An invariant second variation in optimal control
STEFANI, GIANNA;ZEZZA, PIERLUIGI
1998
Abstract
For an optimal control problem we define a second variation which is invariant under change of coordinates, and realize it as a linear-quadratic problem. When the strong Legendre condition is satisfied we give a complete Hamiltonian characterization of the index and of the nullity of the second variation.
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