Geodesic
Optimal control of some oscillating systems
Theoretical and applied mechanics, Tome 2 (1976) no. 1, p. 25 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Optimal motions of dynamical oscillating systems are considered. In the first part of the paper a general approach is developed for optimal control of nonlinear systems with a small parameter. The system is assumed to have the standard form of systems with a rotating phase. Problem of optimal control is reduced to two-point boundary problem which is analysed by means of Kry-lov-Bogoljubov asymptotic method of averaging. In the second part of the paper the explicit solution of one problem of optimal control is given. The system consists of a pendulum attached to a body moving with restricted velocity. Minimal time optimal solution which extinguish oscillations of the pendulum in the final state has several intervals of constant velocity. The results were applied for optimal control of cranes carrying swinging loads. 
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     author = {F. L. Chernousko},
     title = {Optimal control of some oscillating systems},
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F. L. Chernousko. Optimal control of some oscillating systems. Theoretical and applied mechanics, Tome 2 (1976) no. 1, p. 25 . http://geodesic.mathdoc.fr/item/TAM_1976_2_1_a3/