Geodesic
Geometric approach to the problem of optimal scalar control of two nonsynchronous oscillators
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Geometry, and Combinatorics, Tome 215 (2022), pp. 40-51

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The problem of optimal scalar control of a system of two independent harmonic oscillators is considered. For the solution, methods of geometric control theory are used. The vertical subsystem of the Hamiltonian system is examined. Optimal solutions are found in control classes with various number of switchings. Analytical results are illustrated by simulation.
Keywords: geometric theory, optimal control, harmonic oscillator, Pontryagin's maximum principle, Lie algebra. 
@article{INTO_2022_215_a3,
     author = {L. M. Berlin and A. A. Galyaev and P. V. Lysenko},
     title = {Geometric approach to the problem of optimal scalar control of two nonsynchronous oscillators},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {40--51},
     publisher = {mathdoc},
     volume = {215},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_215_a3/}
}
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L. M. Berlin; A. A. Galyaev; P. V. Lysenko. Geometric approach to the problem of optimal scalar control of two nonsynchronous oscillators. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Geometry, and Combinatorics, Tome 215 (2022), pp. 40-51. http://geodesic.mathdoc.fr/item/INTO_2022_215_a3/