Vladimir Petukhov
Pereslavl-Zalessky, Yaroslavl Region, 152020 Russia
Ailamazyan Program Systems Institute, Russian Academy of Sciences
Publications:
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Petukhov V. S., Sachkov Y. L.
The Lorentzian Problem on 2-Dimensional de Sitter Space
2024, Vol. 20, no. 4, pp. 619-633
Abstract
This paper considers the Lorentzian optimal control problem on two-dimensional de Sitter
space. Normal and abnormal optimal trajectories are studied using the Pontryagin maximum
principle. Attainable sets, spheres and distance in the Lorentzian metric are computed. Killing
vector fields and isometries are described.
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Sachkov Y. L., Stepanov D. N., Petukhov V. S.
Abstract
The simplest almost Riemannian problem with a Martinet point is studied. Extremal and
optimal trajectories are studied by analytic, symbolic, and numeric techniques.
Analytically the following results were obtained: existence of optimal trajectories was
proved, absence of abnormal trajectories was shawn, a Hamiltonian system for normal extremals
was derived, its symmetry and Maxwell points was described. Symbolically all polynomial integrals
of the Hamiltonian system of degree not greater than 54 were described. Numerically the
optimal synthesis was constructed.
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