Мақаланы E-mail арқылы жіберу SINGULARLY PERTURBED OPTIMAL TRACKING PROBLEM
- Авторлар: Sobolev V.1
-
Мекемелер:
- Samara National Research University
- Шығарылым: Том 60, № 4 (2024)
- Беттер: 561-576
- Бөлім: Articles
- URL: https://journals.rcsi.science/0374-0641/article/view/257630
- DOI: https://doi.org/10.31857/S0374064124040105
- EDN: https://elibrary.ru/OWPHWV
- ID: 257630
Дәйексөз келтіру
Ашық рұқсат
Рұқсат берілді
Тек жазылушылар үшін
Аннотация
We consider a singularly perturbed optimal tracking problem with a given etalon trajectory in the case of incomplete information about the state vector in the presence of external disturbances. To analyze the differential equations that arise when solving this problem, the decomposition method is used, which is based on the technique of integral manifolds of fast and slow motions.
Негізгі сөздер
Әдебиет тізімі
- Васильева, А.Б. Сингулярные возмущения в задачах оптимального управления / А.Б. Васильева, М.Г. Дмитриев // Итоги науки и техники. Сер. Мат. анализ. — М. : ВИНИТИ, 1982. — Т. 20. — С. 3–78.
- Дмитриев, М.Г. Сингулярные возмущения в задачах управления / М.Г. Дмитриев, Г.А. Курина // Автоматика и телемеханика. — 2006. — № 1. — С. 3–51.
- Naidu, D.S. Singular perturbations and time scales in control theory and applications: an overview / D.S. Naidu // Dynam. Continuous, Discrete and Impulsive Syst. Ser. B: Appl. & Algorithms. — 2002. — V. 9, № 2. — P. 233–278.
- Sobolev, V.A. Integral manifolds and decomposition of singularly perturbed system / V.A. Sobolev // Syst. Control Lett. — 1984. — V. 5. — P. 169–179.
- Воропаева, Н.В. Геометрическая декомпозиция сингулярно возмущённых систем / Н.В. Воропаева, В.А. Соболев. — М. : Физматлит, 2009. — 256 с.
- Kokotovi´c, P.V. Singular Perturbation Methods in Control. Analysis and Design / P.V. Kokotovi´c, H.K. Khalil, J. O’Reily. — London : Academic Press, 1986. — 371 p.
- Sontag, E. Mathematical Control Theory: Deterministic Finite-Dimensional Systems / E. Sontag. — 2nd ed. — New York : Springer-Verlag, 1998. — 531 p.
- Prasov, A. Tracking performance of a highgain observer in the presence of measurement noise / A. Prasov, H.K. Khalil // Int. J. Adapt. Control Signal Proc. — 2016. — V. 30, № 8–10. — P. 1228–1243.
- Соболев, В.А. Сингулярные возмущения в линейно-квадратичной задаче оптимального управления / В.А. Соболев // Автоматика и телемеханика. — 1991. — № 2. — С. 53–64.
- Воропаева, Н.В. Конструктивный метод расщепления нелинейных сингулярно возмущённых дифференциальных систем / Н.В. Воропаева, В.А. Соболев // Дифференц. уравнения. — 1995. — Т. 31, № 4. — С. 569–578.
- Vasil’eva, A.B. and Dmitriev, M.G., Singular perturbations in optimal control problems, J. Math. Sci., 1986, vol. 34, pp. 1579–1629.
- Dmitriev, M.G. and Kurina, G.A., Singular perturbations in control problems, Autom. Remote Control, 2006, vol. 67, pp. 1–43.
- Naidu, D.S., Singular perturbations and time scales in control theory and applications: an overview, Dynam. Continuous, Discrete and Impulsive Syst. Ser. B: Appl. & Algorithms, 2002, vol. 9, pp. 233–278.
- Sobolev, V.A., Integral manifolds and decomposition of singularly perturbed system, Syst. Control Lett., 1984, vol. 5, pp. 169–179.
- Voropaeva, N.V. and Sobolev, V.A., Geometricheskaya dekompozitsiya singulyarno vozmushchennykh sistem (Geometric decomposition of singularly perturbed systems), Moscow: Fizmatlit, 2009.
- Kokotovi´c, P.V., Khalil, H.K., and O’Reily, J., Singular Perturbation Methods in Control. Analysis and Design, London: Academic Press, 1986.
- Sontag, E., Mathematical Control Theory: Deterministic Finite-Dimensional Systems, 2nd ed., New York: Springer-Verlag, 1998.
- Prasov, A. and Khalil, H.K., Tracking performance of a highgain observer in the presence of measurement noise, Int. J. Adapt. Control Signal Proc., 2016, vol. 30, no. 8–10, pp. 1228–1243.
- Sobolev, V.A., Singular perturbations in a linear-quadratic problem of optimal control, Autom. Remote Control, 1991, vol. 52, pp. 180–189.
- Voropaeva, N.V. and Sobolev, V.A., A constructive method for splitting nonlinear singularly perturbed differential systems, Differ. Equat., 1995, vol. 31, no. 4, pp. 528–537.
