Geodesic
One problem of the optimal control of a system with aftereffect in conditions of conflict
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2008), pp. 65-70 
N. N. Krasovskii; A. N. Kotel'nikova. One problem of the optimal control of a system with aftereffect in conditions of conflict. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2008), pp. 65-70. http://geodesic.mathdoc.fr/item/VUU_2008_2_a23/
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     title = {One problem of the optimal control of a~system with aftereffect in conditions of conflict},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
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In the paper a time-optimal control problem is considered. Sufficient conditions for local optimality are obtained which are linked with necessary conditions of Pontryagin's maximum principle under assumption of total controllability of a system in variations. The problem is studied for a system described by a vector differential equation either ordinary or with aftereffect. In the case of conflict control, the optimal control problem is discussed for a criterion of the minmax-maxmin time when the system attains a given state. The model example is given and the corresponding numerical experiment is discussed.

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