Application of hybrid multi-agent interpolation search method to the satellite stabilization problem


DOI: 10.34759/trd-2021-117-10

Аuthors

Panteleyev A. V.1*, Karane M. S.2**

1. ,
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: avpanteleev@inbox.ru
**e-mail: mmkarane@mail.ru

Abstract

The article regards the problem solution of satellite stabilization using the algorithm for finding the optimal open-loop control based on application of the expansion in terms of the system of basis functions and the multi-agent method.

Multi-agent algorithms are quite popular now and used in various fields of science. Multi-agent algorithms are not rigorously justified and convergence guarantee, however they are successfully applied in practice and demonstrate acceptable results in reasonable computational time. The article proposes a hybrid multi-agent interpolation search algorithm based on the Bezier, Catmull-Rom and B-splines interpolation curves construction. The curves are being constructed based on information on the agents, form the current population, position. In addition, the algorithm needs to solve the problems of one-dimensional parametric optimization to realize the exploratory and frontal search. Beyond that point, the described multi-agent method employs the ideas of swarm intelligence and migration algorithms.

Besides, the algorithm under consideration for the optimal open-loop control search is based on application of the expansion in terms of the system of basis functions. This approach is quite popular and actively used in the spectral method for nonlinear control systems analysis and synthesis. The authors propose to search for the optimal open-loop control in the form of a saturation function, which argument is a linear combination of the given basis functions with some coefficients to be found. Particularly, piecewise constant, piecewise linear, quadratic and cubic splines are being used as basis functions. In addition, the saturation function should guarantee the specified constraints fulfillment on the parallelepipedic-type control.

Based on the proposed algorithm, the software for the optimal open-loop control search has been developed, and its algorithm efficiency has been studied when solving the problem of position stabilizing of a satellite driven by engines. Comparative analysis of the effect of basis system selection was performed as well. As it can be seen from the numerical experiment, the algorithm successfully copes with the problem of the satellite position stabilizing and finds a solution close to optimal when using all the above-mentioned systems of basis functions. In addition, the interpolation method parameters were selected so that to achieve a high accuracy of the applied problem being solved.

Keywords:

optimal open-loop control, multi-agent algorithms, optimization, software, satellite stabilization

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