Improvement of variational-gradient method in dynamical systems of automated control for integro-differential models

2019;
: pp. 344–357
https://doi.org/10.23939/mmc2019.02.344
Received: May 15, 2019
Revised: July 11, 2019
Accepted: July 11, 2019

Mathematical Modeling and Computing, Vol. 6, No. 2, pp. 344–357 (2019)

1
State Ecological Academy of Postgraduate Education and Management
2
Lesya Ukrainka East European National University
3
State University of Telecommunications
4
State University of Telecommunications
5
State University of Telecommunications
6
Kyiv National Economic University named after Vadym Hetman

The dynamical systems given by integro-differentiation models with K-symmetric K-positive-definite operator are considered.  The variational-gradient method was applied to those models.  The analysis showed that the implementation of this method does not require knowledge of the operator spectrum, in addition, it has a better convergence rate and is more resistant to disturbances than gradient methods.  The theorem is proved in this paper, which allows us to draw conclusions about the effectiveness of the application of the variational-gradient method for the research of control problems.  Investigation of an integro-differential model with a K-positive-definite K-symmetric operator using the variational-gradient method will increase the efficiency of information processing in the processes of control and research of dynamic systems.  Application of the variational-gradient method to the control tasks will allow expanding the range of tasks under consideration.  It is noted that the development of modern technologies entails an increase in the complexity of control objects, an increase in the quality requirements and the accuracy of control due to the increase in the cost of control error.  This makes to be essential further development and improvement of methods that solve the problems of optimal control, for example, unmanned aerial vehicles.  As the model example, the application of the variational-gradient method to the models of automated control systems for unmanned aerial vehicles is considered.

  1. Barabash O. V., Dakhno N. B., Shevchenko H. V., Neshcheret O. S., Musienko A. P.  Information Technology of Targeting: Optimization of Decision Making Process in a Competitive Environment.  International Journal of Intelligent Systems and Applications. 9 (12), 1--9 (2017).
  2. Mashkov O. A., Al-Tameemi Raheem Qasim Naser, Lami Juhi Hussein, Kosenko V. R.  Application informal approach to contriol complex dynamic systems.  Control, navigation and communication systems. 4, 31--37 (2015), (in Ukrainian).
  3. Kucherov D. P.  On some methods and algorithms for calculating matrix exponential in problems of control system dynamics analysis.  Upravlyayushchie Sistemy i Mashiny. 11--17 (2001), (in Russian).
  4. Chakraborty A., Konar A.  Mathematical Modeling and Analysis of Dynamical Systems. In: Emotional Intelligence.  Studies in Computational Intelligence. Vol. 234. Berlin, Heidelberg, Springer (2009).
  5. Barabash O., Kravchenko Y., Mukhin V., Kornaga Y., Leshchenko O.  Optimization of Parameters at SDN Technologie Networks.  International Journal of Intelligent Systems and Applications. 9 (9), 1--9 (2017).
  6. Gramajo G., Shankar P.  An Efficient Energy Constraint Based UAV Path Planning for Search and Coverage.  International Journal of Aerospace Engineering. 2017, Article ID 8085623, 13 pages (2017).
  7. Mashkov O. A., Mamchur Yu. V.  Analytical estimation of the quality of the control process on the simulators of a remote pilot airplane with algorithm based on the solution of the reverse dynamics problems.  Aerospace technologies. 2, 59--62 (2017).
  8. Obidin D., Ardelyan V., Lukova-Chuiko N., Musienko A.  Estimation of functional stability of special purpose networks located on vehicles.  2017 IEEE 4th International Conference Actual Problems of Unmanned Aerial Vehicles Developments (APUAVD), Kiev. 167--170 (2017).
  9. Barabash O., Lukova-Chuiko N.,Sobchuk V., Musienko A.  Application of Petri Networks for Support of Functional Stability of Information Systems.  2018 IEEE 1st International Conference on System Analysis and Intelligent Computing, SAIC 2018 - Proceedings.  Kiev. 167--170 (2017).
  10. Boichuk O., Holovats'ka I.  Boundary-Value Problems for Systems of Integrodifferential Equations.  Journal of Mathematical Sciences. 203 (3),  306--321 (2014).
  11. Perestyuk M. O., Kasyanov P. O., Zadoyanchuk N. V.  On Faedo--Galerkin method for evolution inclusions with $W_{\lambda_0}$-pseudomonotone maps.  Memoirs on Differential Equations and Mathematical Physics. 44, 105--132 (2008).
  12. Tuyrin V., Barabash O., Openko P., Sachuk I., Dudush A.  Informational support system for technical state control of military equipment.  2017 IEEE 4th International Conference Actual Problems of Unmanned Aerial Vehicles Developments (APUAVD), Kiev. 230--232 (2017).
  13. Kucherov D., Kozub A.  Model of UAV as agent of multiagent system.  2018 IEEE 9th International Conference on Dependable Systems, Services and Technologies (DESSERT), Kiev. 343--347 (2018).
  14. Kucherov D., Kozub A. Rasstrygin A.  Setting the PID Controller for Controlling Quadrotor Flight: a Gradient Approach.  2018 IEEE 5th International Conference on Methods and Systems of Navigation and Motion Control, MSNMC. 90--93 (2018).
  15. Luchka A. Yu., Noschenko O. E., Tuhalevskaya N. I.  Variational Gradient Method.  USSR Computational Mathematics and Mathematical Physics.  24 (4),  1--6 (1984).
  16. Barabash O., Dakhno N., Shevchenko H., Sobchuk V.  Integro-Differential Models of Decision Support Systems for Controlling Unmanned Aerial Vehicles on the Basis of Modified Gradient Method.  2018 IEEE 1st International Conference on System Analysis and Intelligent Computing, SAIC, 94--97 2018.
  17. Barabash O. V., Dakhno N. B., Shevchenko H. V., Majsak T. V.  Dynamic models of decision support systems for controlling UAV by two-step variational-gradient method.  2017 IEEE 4th International Conference on Actual Problems of Unmanned Aerial Vehicles Developments, APUAVD. 108--111 (2017).
  18. Petryshyn W. V.  On a class of K-p.d. and non-K-p.d. operators and operator equations.  Journal of Matheamatical analysis and applications.  10 (1),  1--24 (1965).
  19. Lutsenko A. V., Skorik V. A.  Funkcija Grina i ee primenenie.  Har'kov, Har'kovskij nacional'nyj universitet im. V.N. Karazina (2002), (in Russian).
  20. Kadets V.  A Course in Functional Analysis and Measure Theory.  Springer, Cham (2018).
  21. Lenkov S. V., Khoroshko V. O., Dakhno N. B.  Odnokrokovyi variatsiino-hradiientnyi metod shchodo matematychnykh modelei kompleksnykh system zakhystu informatsii.  Visnyk Kyivskoho natsionalnoho universytetu imeni Tarasa Shevchenka. Viiskovo-spetsialni nauky.  22, 10--13 (2009), (in Ukrainian).
  22. Mashkov O. A., Durniak B. V., Mamchur Yu. V., Timchenko O. V.  Syntez alhorytmu prohramnoho keruvannia na trenazheri dystantsiino pilotovanoho litalnoho aparata na osnovi alhorytmichnoi protsedury rishennia zvorotnoi zadachi dynamiky (stokhastychna postanovka).  Modeliuvannia ta informatsiini tekhnolohii. 82, 166--176 (2018), (in Ukrainian).