QUADRATIC CONDITIONS FOR A PONTRYAGIN MINIMUM IN AN OPTIMUM CONTROL PROBLEM LINEAR IN THE CONTROL. I: A DECODING THEOREM
А. В. Дмитрук · Mathematics of the USSR-Izvestiya · 1987
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.