ELLIPSOIDAL APPROXIMATION FOR AREAS OF PARAMETRICAL UNCERTAINTY OF TECHNICAL CONDITIONS OF ROBOTIC COMPLEX

ELLIPSOIDAL APPROXIMATION FOR AREAS OF PARAMETRICAL UNCERTAINTY OF TECHNICAL CONDITIONS OF ROBOTIC COMPLEX

A.M. Vinogradenko
PhD in Technical Sciences, Military Academy of the Signal Corps named after S.M. Budjonny, Associate Professor, Doctoral Candidate, 3, Tikhoretsky pr., Saint-Petersburg, 194064, Russia, tel.: +7(981)833-92-31, This email address is being protected from spambots. You need JavaScript enabled to view it.

Received 30 July 2018

Abstract
The expediency of ellipsoidal approximation for area of parametrical uncertainty of technical condition of a robotic complex at various stages of life cycle, in which with set probability there are values of the measured output parameters, is shown. The model of affine transformation of area of uncertainty in space of parameters taking into account external indignations and an error of measurements is presented. The technique of reduction of a robotic complex to the surface of a multidimensional ellipsoid for the minimum time is offered.

Key words
Technical condition, robotic complex, control, controlled parameters, area of uncertainty.

https://doi.org/10.31776/RTCJ.6306 

Bibliographic description
Vinogradenko, A. (2018). Ellipsoidal approximation for areas of parametrical uncertainty of technical conditions of robotic complex. Robotics and Technical Cybernetics, 3(20), pp.53-60.

UDC identifier:
517.977

References

  1. Budko, P., Vinogradenko, A., Goydenko, V. and Zhukov, G. (2016). Determination of critical condition of a sea robotic complex according to the multi-stage procedure of control on the basis of use of veyvlet-transformations. Sea radio electronics, 4(58), pp.18-23. (in Russian).
  2. Vinogradenko, A., Ladonkin, О. and Yurov, А. (2015). The system of monitoring of technical condition of military mobile objects with use of wireless technologies. T-Comm: Telecommunications and transport, 1, pp.51-55. (in Russian).
  3. Abramov, O. and Dimitrov, B. (2017). Reliability design in gradual failures: a functional-parametric approach. Reliability: Theory&Application, 4(47), pp.39-48.
  4. Abramov, O. (2016) Choosing Optimal Values of Tuning Parameters for Technical Devises and Systems. Automation and Remote Control, 4, pp.594-603.
  5. Budko, P., Vinogradenko, A., Kuznetsov, S. and Goydenko, V. (2017). Realization of a Method of Multilevel Complex Control of Technical Condition of a Sea Robot. Systems of Control, Communication and Security, 4, pp.71-101. Available at: http://sccs.intelgr.com/archive/2017-04/04-Budko.pdf.
  6. Borgonovo, E. (2007). A new uncertainty importance measure. Reliability Engineering & System Safety, 6(92), pp.771-784.
  7. Vinogradenko, A., Vasil'ev, V., Veselovsky, А. and Мezhenov, А. (2018). Diagnosing and identification of technical condition of the distributed radio-electronic systems. Automation and instrumentation: problems, decisions, 3, pp.32-41. (in Russian).
  8. Akulenko, L. and Shmatkov, А. (2018). Reduction of a dynamic object, minimum in time, on an ellipsoid. News of the Russian Academy of Sciences: theory and control systems, 1, pp.64-72. (in Russian).
  9. Abramov, O. and Nazarov, D. (2016). Condition-based maintenance by minimax criteria. Applied Mathematics in Engineering and Reliability. In: Proceedings of the 1st International Conference on Applied Mathematics in Engineering and Reliability, pp. 91-94.
  10. Fedorenko,V., Vinogradenko, A., Samoylenko, V., Samoylenko, I. and Sharipov, I. (2018). Minimization of the parametric uncertainty region for a system under repair. In: Proceedings of the 21st International Conference on Soft Measurements and Computing, pp.35-38. (in Russian).
  11. Akulenko, L. and Shmatkov, А. (2017). Reduction of a dynamic object, optimum on speed, on an ellipsoid surface in multidimensional space. DAN, 1, pp.29-33. (in Russian).
  12. Bertsekas, D., Rhodes, J. (1971). Recursive state estimation for a setmembership description of uncertainty. IEEE Trans. Automat. Control, 2, pp.117-128.
  13. Fedorenko, V. (2001). Optimization of restoration of a technical control system in the conditions of uncertainty of her state. Management information systems on railway transport, 4, pp.56-58. (in Russian).
  14. Kurzhansky, А. (1977). Upravlenie i nablyudenie v usloviyah neopredelyonnosty [Management and observation in the conditions of uncertainty]. Moscow, Russia: Science.
  15. Ovseevich, А., Taraban'ko, Y. (2007). Obvious formulas for the ellipsoids approximating areas of approachability. News of the Russian Academy of Sciences: theory and control systems, 2, pp.33-34. (in Russian).
  16. Chernousko, F. (1988). Otsenivanie fazovogo sostoyaniya dinamicheskih system [Estimation of a Phase Condition of Dynamic Systems]. Moscow, Russia: Science.
  17. Chernousko, F. (1994). State Estimation for Dynamic Systems. Boca Raton, Florida, USA: CRC Press.
  18. Filippov, A. (1992). Ellipsoidal estimates for a solution of a system of differential aquations. Interval Computations, 2, рр.6-17. (in Russian).
  19. Kurzhanski, A. and Varaiya, P. (2002). On ellipsoidal techniques for reachability analysis. Part I: External approximations [Optimiz. Methods&Software], 2, pp.177-206. (in Russian).
  20. Filippova, Т. (2010). The differential equations of ellipsoidal estimates of sets of approachibility of the nonlinear dynamic operated system. Works of Matamatiki Mekhaniki Institute of the Ural Office of the Russian Academy of Sciences, 1, pp.223-232. (in Russian).
  21. Filippova, T. and Berezina, E. (2008). On state estimation approaches for uncertain dynamical systems with quadratic nonlinearity: theory and computer simulations. Lecture Notes in Computer Science, 4818, pp.326-333.
  22. Polyak, B., Nazin, S., Durieu, C. and Walter, E. (2004). Ellipsoidal parameter or state estimation under model uncertainty. Automatica, 40(7), pp.1171-1179. DOI: 10.1016/j.automatica.2004.02.014.
  23. Budko, P., Vinogradenko, A., Goydenko, V. and Timoshenko, L. (2018). Method of multidimensional statistical control of technical condition of the radio-electronic equipment on the basis of the integration of indications of several types of sensors. Sensors & systems, 3(223), pp.3-11. (in Russian).
  24. Vinogradenko, А., Veselovsky, А. and Bur'yanov, О. (2016). Operating control of technical condition of mobile electrotechnical objects. In: Proceedings of the 3 All-Russian scientific and practical conference «Modern problems of creation and operation of Arms of the Military and Special Equipment», pp. 178-184. (in Russian).
  25. Budko, P., Vinogradenko, A., Veselovsky, А. and Bur'yanov, О. (2017). Model of the automated control system of technical condition of land robotic complexes. Proceedings of the 2 scientific and practical conference «Problems of technical providing troops in modern conditions», pp.145-149. (in Russian).
  26. Lluís, R., Assumpta, S. and Federico, T. (2002). An ellipsoidal calculus based on propagation and fusion. In: IEEE transactions on systems, man, and cybernetics – part b: cybernetics, 4, pp.430-442.
  27. Pontryagin, L., Boltyansky, V., Gamkrelidze, R. and Mischenko, Е. (1983). Matematicheskaya teoriya optimal'nih protsessov [Mathematical theory of optimum processes]. Moscow, Russia: Science.
Editorial office address: 21, Tikhoretsky pr., Saint-Petersburg, Russia, 194064, tel.: +7(812) 552-13-25 e-mail: zheleznyakov@rtc.ru