Cite item


In the proposed cycle of work, we begin the study of the motion of an aircraft which is described bynonlinear ordinary differential equations. Based on these equations, the probable malfunctions in the motioncontrol system are classified, the concepts of reference malfunctions and their neighborhoods are introduced,the mathematical modeling of these malfunctions and their neighborhoods is carried out, the concept ofdiagnostic space is introduced, and the mathematical structure of this space is defined. Proposed work isthe first in the cycle, therefore, the classification of malfunctions is given. This activity is also a preparatorypart of the diagnostic problem, which can be represented in the form of two successively solved problems,i.e., control problem, that is the problem of determining the presence of a malfunction in the system, anddiagnostic problem, that is the recognition problem of malfunction specification. This activity is just anillustration of the proposed approach.

About the authors

M. V. Shamolin

Lomonosov Moscow State University

Author for correspondence.
ORCID iD: 0000-0002-9534-0213

Doctor of Physical and Mathematical Sciences, full professor, leading researcher of the Institute of Mechanics, academic of the Russian Academy of Natural Sciences


  1. Borisenok I.T., Shamolin M.V. . Fundament. iprikl. matem. , 1999, Vol. 5, no. 3, pp. 775–790. Availableat: .
  2. Shamolin M.V. Nekotorye zadachi differentsial’noi i topologicheskoi diagnostiki, Izdanie 2-e, pererab. i dopoln.. M.: Ekzamen,2007. Available at: .
  3. Shamolin M.V. Foundations of Differential and Topological Diagnostics. Journal of Mathematical Sciences, 2003,Vol. 114, no. 1, pp. 976–1024. doi: 10.1023/A:1021807110899 .
  4. Parkhomenko P.P., Sagomonian E.S. Osnovy tekhnicheskoi diagnostiki . M.:Energiya, 1981. Available at: : .
  5. Mironovskii L.A. Funktsional’noe diagnostirovanie dinamicheskikh sistem . Avtomatika i telemekhanika, 1980, Issue 8, pp. 96–121. Available at: .
  6. Okunev Yu.M., Parusnikov N.A. Strukturnye i algoritmicheskie aspekty modelirovaniya dlya zadach upravleniya. M.: Izd-vo MGU, 1983. .
  7. Chikin M.G. Sistemy s fazovymi ogranicheniyami . Avtomatika i telemekhanika, 1987,Issue 10, pp. 38–46. Available at: .
  8. Zhukov V.P. O dostatochnykh i neobkhodimykh usloviyakh asimptoticheskoi ustoichivosti nelineinykh dinamicheskikhsistem .Avtomatika i telemekhanika , 1994, Issue 3, pp. 321–330. Availableat: .
  9. Zhukov V.P. O dostatochnykh i neobkhodimykh usloviyakh grubosti nelineinykh dinamicheskikh sistem v smyslesokhraneniya kharaktera ustoichivosti . Avtomatika i telemekhanika ,2008, Volume 69, Issue 1, pp. 27–35. doi: 10.1134/S0005117908010037 .
  10. Zhukov V.P. O reduktsii zadachi issledovaniya nelineinykh dinamicheskikh sistem na ustoichivost’ vtorym metodom Lyapunova . Avtomatika i telemekhanika , 2005, Vol. 66, Issue 12, pp. 1916–1928. doi: 10.1007/s10513-005-0224-9 .
  11. Borisenok I.T., Shamolin M.V. Reshenie zadachi differentsial’noi diagnostiki metodom statisticheskikh ispytanii. Vestnik MGU. Ser. 1.Matematika. Mekhanika , 2001, no. 1, pp. 29–31. .
  12. Beck A., Teboulle M. Mirror Descent and Nonlinear Projected Subgradient Methods forConvex Optimization. Oper. Res. Lett., 2003, Vol. 31, no. 3, pp. 167–175. Available at: .
  13. Ben-Tal A., Margalit T., Nemirovski A. The Ordered Subsets Mirror Descent Optimization Methodwith Applications to Tomography. SIAM Journal on Optimization, 2001, Vol. 12, No. 1, pp. 79–108. doi: 10.1137/S1052623499354564 .
  14. Su W., Boyd S., Candes E. A Differential Equation for Modeling Nesterov’s Accelerated Gradient Method: Theoryand Insights. Journal of Machine Learning Research, 2016, no. 17(153), pp. 1–43. Available at: arXiv:1503.01243 .
  15. Shamolin M.V. Diagnostika girostabilizirovannoi platformy, vklyuchennoi v sistemu upravleniya dvizheniemletatel’nogo apparata . Elektronnoe modelirovanie , 2011, Vol. 33, no. 3, pp. 121–126. Available at: .
  16. Shamolin M.V. Diagnostika dvizheniya letatel’nogo apparata v rezhime planiruyushchego spuska . Elektronnoe modelirovanie , 2010, Vol. 32,no. 5, pp. 31–44. URL: .
  17. Fleming W.H. Optimal Control of Partially Observable Diffusions. SIAM Journal of Control and Optimization,1968, Vol. 6, No. 2, pp. 194–214. URL:
  18. Choi D.H., Kim S.H., Sung D.K. Energy-efficient Maneuvering and Communication of a Single UAV-based Relay.IEEE Trans. Aerosp. Electron. Syst., 2014, Vol. 50, no. 3, pp. 2119–2326.
  19. Ho D.-T., Grotli E.I., Sujit P.B., Johansen T.A., Sousa J.B. Optimization of Wireless Sensor Network and UAVData Acquisition. Journal of Intelligent & Robotic Systems, April 2015, Vol. 78, Issue 1, pp. 159–179. doi: 10.1007/s10846-015-0175-5 .
  20. Ceci C., Gerardi A., Tardelli P. Existence of Optimal Controls for Partially Observed JumpProcesses. Acta Applicandae Mathematica, November 2002, Volume 74, Issue 2, pp. 155–175. doi: 10.1023/A:1020669212384 .
  21. Rieder U., Winter J. Optimal Control of Markovian Jump Processes with Partial Information and Applications toa Parallel Queueing Model. Mathematical Methods of Operations Research, December 2009, Vol. 70, pp. 567–596.doi: 10.1007/s00186-009-0284-7 .
  22. Chiang M., Tan C.W., Hande P., Lan T. Power control in wireless cellular networks. Foundations and Trendsin Networking, 2008, Vol. 2, no. 4, pp. 381–533. doi: 10.1561/1300000009 .
  23. Altman E., Avrachenkov K., Menache I., Miller G., Prabhu B.J., Shwartz A. Power control in wireless cellularnetworks. IEEE Trans. Autom. Contr., 2009, Vol. 54, no. 10, pp. 2328–2340 .
  24. Ober R.J. Balanced Parameterization of Classes of Linear Systems. SIAM Journal on Control and Optimization,1991, Vol. 29, no. 6, pp. 1251–1287. doi: 10.1137/0329065 .
  25. Ober R.J., McFarlane D. Balanced Canonical Forms for Minimal Systems: A normalized Coprime FactorApproach. Linear Algebra and its Applications, 1989, Vol. 122-124, pp. 23–64. doi: 10.1016/0024-3795(89)90646-0 .
  26. Antoulas A.C., Sorensen D.C., Zhou Y. On the Decay Rate of Hankel Singular Values and Related Issues. Systems& Control Letters, 2002, Vol. 46, Issue 5, pp. 323–342. doi: 10.1016/S0167-6911(02)00147-0 .
  27. Wilson D.A. The Hankel Operator and its Induced Norms. International Journal of Control, 1985, Vol. 42,pp. 65–70. DOI: /10.1080/00207178508933346.
  28. Anderson B.D. O., Jury E.I., Mansour M. Schwarz Matrix Properties for Continuous and Discrete Time Systems.International Journal of Control, 1976, 23(1), pp. 1–16. doi: 10.1080/00207177608922133.
  29. Peeters R., Hanzon B., Olivi M. Canonical Lossless State-Space Systems: Staircase Forms and theSchur Algorithm. Linear Algebra and its Applications, 2007, Vol. 425, no. 2-3, pp. 404–433. doi: 10.1016/j.laa.2006.09.029.
  30. Tang X., Wang S. A Low Hardware Overhead Self-diagnosis Technique Using ReedSolomon Codes forSelf-repairing Chips. IEEE Transactions on Computers, 2010, Volume 59, Issue 10, pp. 1309–1319. doi: 10.1109/TC.2009.

Copyright (c) 2019 М. В. Шамолин

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies