SINGULARLY PERTURBED OPTIMAL TRACKING PROBLEM

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Resumo

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.

Sobre autores

V. Sobolev

Samara National Research University

Email: hsablem@gmal.com
Russia

Bibliografia

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  4. Sobolev, V.A. Integral manifolds and decomposition of singularly perturbed system / V.A. Sobolev // Syst. Control Lett. — 1984. — V. 5. — P. 169–179.
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  9. Соболев, В.А. Сингулярные возмущения в линейно-квадратичной задаче оптимального управления / В.А. Соболев // Автоматика и телемеханика. — 1991. — № 2. — С. 53–64.
  10. 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.
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  12. Dmitriev, M.G. and Kurina, G.A., Singular perturbations in control problems, Autom. Remote Control, 2006, vol. 67, pp. 1–43.
  13. 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.
  14. Sobolev, V.A., Integral manifolds and decomposition of singularly perturbed system, Syst. Control Lett., 1984, vol. 5, pp. 169–179.
  15. Voropaeva, N.V. and Sobolev, V.A., Geometricheskaya dekompozitsiya singulyarno vozmushchennykh sistem (Geometric decomposition of singularly perturbed systems), Moscow: Fizmatlit, 2009.
  16. Kokotovi´c, P.V., Khalil, H.K., and O’Reily, J., Singular Perturbation Methods in Control. Analysis and Design, London: Academic Press, 1986.
  17. Sontag, E., Mathematical Control Theory: Deterministic Finite-Dimensional Systems, 2nd ed., New York: Springer-Verlag, 1998.
  18. 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.
  19. Sobolev, V.A., Singular perturbations in a linear-quadratic problem of optimal control, Autom. Remote Control, 1991, vol. 52, pp. 180–189.
  20. 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.

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