Mathematics

Reduction of the optimal tracking problem in the presence of noise

V. A. Sobolev<sup>ab

a</sup> Samara National Research University, Samara, Russian Federation
^b Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences (FRC CSC RAS), Moscow, Russian Federation

Abstract: 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.

Keywords: singular perturbations, integral manifolds, integral manifold, optimal tracking, asymptotic expansion, differential equations, fast variables, slow variables.

UDC: 517.928

Received: 12.09.2022
Revised: 25.11.2022
Accepted: 05.12.2022

DOI: 10.18287/2541-7525-2022-28-3-4-32-39