Geodesic
Methods of Simplifying Optimal Control Problems,
Russian journal of nonlinear dynamics, Tome 19 (2023) no. 1, pp. 35-48

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Methods of simplifying optimal control problems by decreasing the dimension of the space of states are considered. For this purpose, transition to new phase coordinates or conversion of the phase coordinates to the class of controls is used. The problems of heat exchange and parametric control of oscillators are given as examples: braking/swinging of a pendulum by changing the length of suspension and variation of the energy of molecules’ oscillations in the crystal lattice by changing the state of the medium (exposure to laser radiation). The last problem corresponds to changes in the temperature of the crystal.
Keywords: change of state variables, problems linear in control, heat exchange with minimal dissipation, parametric control, oscillation of a pendulum
Mots-clés : ensemble of oscillators. 
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A. M. Tsirlin. Methods of Simplifying Optimal Control Problems,. Russian journal of nonlinear dynamics, Tome 19 (2023) no. 1, pp. 35-48. http://geodesic.mathdoc.fr/item/ND_2023_19_1_a2/