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ORBITAL DECOMPOSITIONS OF CONTROL SYSTEMS AND TRAJECTORY PLANNING
- Authors: Chetverikov V.N1
-
Affiliations:
- Bauman Moscow State Technical University
- Issue: Vol 61, No 11 (2025)
- Pages: 1554-1565
- Section: CONTROL THEORY
- URL: https://journals.rcsi.science/0374-0641/article/view/352962
- DOI: https://doi.org/10.7868/S3034503025110093
- ID: 352962
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Abstract
The paper studies the problem of transferring a nonlinear dynamic control system from a given initial state to a given final state. An approach is developed based on constructing such a decomposition of the system, in which the specified problem is transformed into two coupled Cauchy problems. One of these problems has boundary conditions at the initial moment, and the second — at the final moment. The case is considered when the boundary conditions of the problem are imposed only on a part of the state variables. To transform the system into a decomposable form, invertible transformations of the most general type are used — orbital equivalences. The given nontrivial example demonstrates the possibility of implementing the specified approach.
About the authors
V. N Chetverikov
Bauman Moscow State Technical University
Email: chetverikov.vi@yandex.ru
Russia
References
- Крутько, П.Д. Обратные задачи динамики управляемых систем: нелинейные модели / П.Д. Крутько. — М. : Наука, 1988. — 327 с.
- Симметрии и законы сохранения уравнений математической физики / А.В. Бочарова, А.М. Вербовецкий, А.М. Виноградов [и др.]. — 2-е изд., испр. и доп. — М. : Факториал, 2005. — 474 с.
- A Lie–Bäcklund approach to equivalence and flatness of nonlinear systems / M. Fliess, J. Levine, Ph. Martin, P. Rouchon // IEEE Trans. Automat. Control. — 1999. — V. 44, № 5. — Р. 922–937.
- Murray, R. Flat systems. Mini-course / R. Murray, P. Martin, P. Rouchon // ECC' 97 European Control Conf. — Brussels, 1–4 July 1997. — Р. 211–264.
- Белинская, Ю.С. Симметрии, накрытия, декомпозиция систем и терминальное управление / Ю.С. Велинская, В.Н. Четвернюю // Дифференц. уравнения. — 2016. — Т. 52, № 11. — С. 1477–1488.
- Белинская, Ю.С. Метод накрытий для терминального управления и орбитальная декомпозиция систем / IO.C. Benmucka, B.H. Четверяков // Дифференц. уравнения. — 2018. — T. 54, № 4. — C. 502–513.
- Chetverikov, V.N. Orbital decompositions and integrable pseudosymmetries of control systems / V.N. Chetverikov // Automatica. — 2022. — V. 139. — Art. 110189.
- Respondek, W. On decomposition of nonlinear control systems / W. Respondek // Systems & Control Letters. — 1982. — V. 1. — P. 301–308.
- Isidori, A. Nonlinear Control Systems / A. Isidori. — Berlin : Springer, 1995. — 549 p.
- Chetverikov, V.N. On the structure of integrable C-fields / V.N. Chetverikov // Differential Geom. Appl. — 1991. — V. 1. — P. 309–325.
- Соколов, В.В. Псевдосимметрии и дифференциальные подстановки / В.В. Соколов // Функц. анализ и его прил. — 1988. — T. 22, № 2. — C. 47–56.
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