The time-optimal problem of steering a triple integrator from an arbitrary point to the origin is considered under constraints on the input control and on one of the state variables. An optimal control is synthesized based on the maximum principle in the Dubovitskii–Milyutin form.
Keywords: control system, time optimality, state constraint, maximum principle, switching points, Lebesgue–Stieltjes measure, optimal synthesis
Received June 3, 2024
Revised July 3, 2024
Accepted July 8, 2024
Elizaveta Voronina, student, Lomonosov Moscow State University, Moscow, 119991 Russia, e-mail: lizok-voronina@mail.ru
Andrei Dmitruk, Dr. Phys.-Math. Sci., Prof., Central Economics and Mathematics Institute RAS, Moscow, 117418 Russia; Lomonosov Moscow State University, Moscow, 119991 Russia, e-mail: optcon@mail.ru
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Cite this article as: E.Yu. Voronina, A.V. Dmitruk. An optimal synthesis for a triple integrator with a state constraint. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2024, vol. 30, no. 3, pp. 68–85.
