Quadratic conditions for a~Pontryagin minimum in an optimum control problem linear in the control.~I: A~decoding theorem

A. V. Dmitruk

Izvestiya. Mathematics , Tome 28 (1987) no. 2, pp. 275-303.

Résumé

The general optimum control problem considered here is linear in the control and without constraints on the control. Quadratic (i.e., second-order) necessary and sufficient conditions are given for the problem to have a minimum in the class of variations bounded in modulus by an arbitrary constant and having small integral. These conditions are stronger than the previously known conditions for a weak minimum, and, like the latter conditions, constitute an adjoining pair, i.e., the sufficient condition differs from the necessary condition only in the strengthening of an inequality. Bibliography: 17 titles.

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