Galerkin method in problems for optimization of quasilinear dynamic stochastic systems with information restrictions

Аuthors

Khrustaliov M. M.^1*, Rumyantsev D. S.^2**, Tsarkov K. A.^3***

1. V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 65, Profsoyuznaya str., Moscow, 117997, Russia
2. Mechanical Engineering Research Institute of the Russian Academy of Sciences, 4, M. Khariton'evskii per., Moscow, 101990, Russia
3. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: mmkhrustalev@mail.ru
**e-mail: dima_rum@mail.ru
***e-mail: k6472@mail.ru

Abstract

Numeric and approximate analytical methods in problems for optimal control of quasilinear stochastic dynamic diffusive systems with information restrictions. Galerkin method in problems for optimization of quasilinear dynamic stochastic systems with information restrictions.
Making an algorithm for solving the optimization problem of quasilinear stochastic dynamic diffusive systems. The purpose of research concludes in synthesis of the simple optimal control. Also it is required to get the result corresponding with the earlier made numeric methods.
It is possible to apply the Galerkin method for solving the tasks with the system of matrix differential equations, received using the known results and earlier made numeric algorithms. Then we can use the resulting solution in the general scheme of optimal control synthesis. Finally, the obtained numeric values of the criteria function can be compared with the known ones.
An algorithm based on Galerkin method for optimal trajectories synthesis in problems of quasilinear stochastic dynamic diffusive systems control has been successfully created. Its application allows to use profitable a computer memory in comparison with the numeric methods. The results obtained in terms of the criteria function values correspond with the previously made numeric algorithms.
The algorithm used for solving the problem of the Earth satellite orbit stabilization, where only some of the state vector components can be accurately measured. This situation may correspond to the partial measuring systems failure. In general, information restrictions conclude in the fact that each control strategy component depends on the apriori given set of accurately measured state vector components and can manifest themselves in the different situations.

Keywords:

optimal control, incomplete feedback, Lagrange method, Galerkin method, Ito stochastic differential equation, probability density, Earth satellite

References

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