Geodesic
Reduction of the optimal tracking problem in the presence of noise
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 28 (2022) no. 3-4, pp. 32-39

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In this paper, the decomposition method based on the theory of fast and slow integral manifolds is used to analyze the optimal tracking problem. We consider a singularly perturbed optimal tracking problem with a given reference trajectory in the case of incomplete information about the state vector in the presence of random external perturbations.
Mots-clés : singular perturbations, fast variables
Keywords: integral manifolds, integral manifold, optimal tracking, asymptotic expansion, differential equations, slow variables. 
V. A. Sobolev. Reduction of the optimal tracking problem in the presence of noise. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 28 (2022) no. 3-4, pp. 32-39. http://geodesic.mathdoc.fr/item/VSGU_2022_28_3-4_a3/
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[1] Sontag E., Mathematical Control Theory: Deterministic Finite-Dimensional Systems, 2nd edition, Springer-Verlag, Inc, New York, 1998 | DOI | MR | Zbl

[2] Vasil'eva A.B., Dmitriev M.G., “Singular perturbations in optimal control problems”, Journal of Soviet Mathematics, 34:4 (1986), 1579–1629 (In Russ.) | DOI | MR | Zbl | Zbl

[3] Dmitriev M.G., Kurina G.A., “Singular perturbations in control problems”, Automation and Remote Control, 67:1 (2006), 1–43 | DOI | MR | Zbl

[4] Naidu D.S., “Singular Perturbations and Time Scales in Control Theory and Applications: An Overview”, Dynamics of Continuous, Discrete and Impulsive Systems. Series B: Applications Algorithms, 9:2 (2002), 233–278 https://www.d.umn.edu/d̃snaidu/Naidu_Survey_DCDISJournal_2002.pdf | MR | Zbl

[5] Sobolev V.A., “Integral manifolds and decomposition of singularly perturbed systems”, System and Control Letters, 5:3 (1984), 169–179 | DOI | MR | Zbl