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

DOI: 10.34759/trd-2021-117-10


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

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



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.


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


  1. Panovskiy V.N., Panteleev A.V. Meta-heuristic interval methods of search of optimal in average control of nonlinear determinate systems with incomplete information about its parameters, Journal of Computer and System Sciences International, 2017, no. 56 (1), pp. 52 - 63. URL:

  2. Luus R. Iterative dynamic programming. Chapman and Hall/CRC, Boca Raton, USA, 2000, 344 p.

  3. Panteleev A.V., Pis’mennaya V.A. Application of a memetic algorithm for the optimal control of bunches of trajectories of nonlinear deterministic systems with incomplete feedback, Journal of Computer and System Sciences International, 2018, no. 57 (1), pp. 25 - 36. URL:

  4. Panteleev A.V., Metlitskaya D.V. An application of genetic algorithms with binary and real coding for approximate synthesis of suboptimal control in deterministic systems, Automation and Remote Control, 2011, no. 72 (11), pp. 2328 - 2338. URL:

  5. Rao A.V. A Survey of Numerical Methods for Optimal Control, Advances in the Astronautical Sciences, 2010, no. 135 (1), pp. 1 – 32.

  6. Fedorenko R.P. Priblizhennoe reshenie zadach optimal'nogo upravleniya (Approximate solution of optimal control problems), Moscow, Nauka, 1978, 488 p.

  7. Nemychenkov G.I. Trudy MAI, 2019, no. 104. URL:

  8. Vernigora L.V., Kazmerchuk P.V. Trudy MAI, 2018, no. 106. URL:

  9. Beheshti Z., Shamsuddin S. M. H. A review of population-based meta-heuristic algorithms, International Journal of Advances in Soft Computing and its Applications, 2013, no. 5 (1), pp. 1 - 35.

  10. Brownlee J. Clever Algorithms: Nature-Inspired Programming Recipes, LuLu, Morrrisvill, USA, 2011, 423 p.

  11. Panteleev A.V., Skavinskaya D.V., Aleshina E.A. Metaevristicheskie algoritmy poiska optimal'nogo programmnogo upravleniya (Meta-heuristic algorithms for finding optimal open-loop control), Moscow, INFRA-M, 2016, 396 p.

  12. Karane M.M.S. Comparative analysis of multi-agent methods for constrained global optimization, IV international conference on information technologies in engineering education, Moscow, Russia, 23–26 October 2018, pp. 128 - 133. DOI: 10.1109/INFORINO.2018.8581711

  13. Pogarskaya T.A. Trudy MAI, 2020, no. 110. URL: DOI: 10.34759/trd-2020-110-18

  14. Rybakov K.A. Solving the nonlinear problems of estimation for navigation data processing using continuous particle filter, Gyroscopy and Navigation, 2019, no. 10 (1), pp. 27 - 34. DOI: 10.17285/0869-7035.2018.26.4.082-095

  15. Averina T., Rybakov K. Systems with regime switching on manifolds, Proceedings of the 2018 14th International Conference “Stability and Oscillations of Nonlinear Control Systems” (Pyatnitskiy’s Conference) (STAB), IEEE, 2018, pp. 1 - 3. DOI: 10.1109/STAB.2018.8408345

  16. Panteleev A.V., Karane M.S. Izvestiya Instituta inzhenernoi fiziki, 2020, no. 3 (57), pp. 74 - 78.

  17. Blum C., Li X. Swarm Intelligence in Optimization, Swarm Intelligence, Natural Computing Series, Springer, Berlin, 2008, pp. 43 - 85. DOI: 10.1007/978-3-540-74089-6_2

  18. Zelinka I. SOMA - Self-Organizing Migrating Algorithm, New Optimization Techniques in Engineering. Studies in Fuzziness and Soft Computing. Springer, Berlin, Heidelberg, 2004, 141 p. URL:

  19. Panteleev A., Karane M. Hybrid multi-agent optimization method of interpolation search, AIP Conference Proceedings 2181, 020028, 2019. URL:

  20. Bacanin N., Pelevic B., Tuba M. Krill herd (KH) algorithm for portfolio optimization. In: Mathematics and Computers in Business, Manufacturing and Tourism, Proceedings of the 14th Intern. Conf. on Mathematics and Computers in Business and Economics (MCBE 13), Baltimore, USA, 2013, pp. 39 – 44.

  21. Gandomi A.H., Alavi A.H. Krill herd: A new bio-inspired optimization algorithm, Communications in Nonlinear Science and Numerical Simulation, 2012, no. 17 (12), pp. 4831 - 4845. DOI: 10.1016/j.cnsns.2012.05.010

  22. Floudas C.A., Pardalos P.M. Encyclopedia of Optimization, Springer US, 2009, 4622 p.

  23. Krylov I.A. Vychislitel'naya matematika i fizika, 1968, no. 8 (1), pp. 284 - 291.

  24. Khrustalev M.M., Khalina A.S. Trudy MAI, 2018, no. 102. URL:

Download — informational site MAI

Copyright © 2000-2022 by MAI