Constrained disturbances suppression in cognitive maps’ impulse processes based on H∞ theory under incomplete measurements of vertices coordinates

Authors

  • Victor D. Romanenko Educational and Scientific Complex "Institute for Applied System Analysis" of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine https://orcid.org/0000-0002-6222-3336
  • Yuriy L. Milyavsky The Department of the Mathematical methods of system analysis of Educational and Scientific Complex "Institute for Applied System Analysis" of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine https://orcid.org/0000-0003-0882-3418

DOI:

https://doi.org/10.20535/SRIT.2308-8893.2017.4.13

Keywords:

cognitive map, impulse process, robust control, H∞-theory, incomplete measurements of coordinates, limited perturbations

Abstract

The problem of controlling an impulse process of a cognitive map, provided that some of the coordinates are not measured, is stated and solved in the paper. It is assumed that non-measurable coordinates are limited, but their probabilistic characteristics are unknown. The control algorithm is based on the adaptation of the H-theory to the conditions of a complex dynamic system in the impulse process mode of a cognitive map. For this purpose, the system is decomposed into measurable and non-measurable subsystems, a target vector of vertices coordinates to be stabilized is chosen, a measurement equation is introduced, and a robust optimality criterion of control is formulated. The method proposed in the paper is verified for the cognitive map of IT company HR management, which has a large number of non-measurable vertices. Based on the computer simulation, the suitability and effectiveness of applying the proposed control method was demonstrated.

Author Biographies

Victor D. Romanenko, Educational and Scientific Complex "Institute for Applied System Analysis" of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv

Victor Romanenko,

Doctor of Science, professor, the vice director of research and education of Educational and Scientific Complex "Institute for Applied System Analysis" of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine.

Yuriy L. Milyavsky, The Department of the Mathematical methods of system analysis of Educational and Scientific Complex "Institute for Applied System Analysis" of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv

Yuriy Milyavsky,

Ph.D., a senior lecturer at the Department of the Mathematical methods of system analysis of Educational and Scientific Complex "Institute for Applied System Analysis" of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine.

References

Innovatsionnoe razvitie sotsial'no-ekonomicheskih sistem na osnove metodologij predvidenija i kognitivnogo modelirovanija / Pod red. G.V. Gorelovoj, N.D. Pankratovoj. — K.: Nauk. dumka, 2015. — 464 s.

Roberts F.S. Diskretnye matematicheskie modeli s prilozhenijami k sotsial'nym, biologicheskim i ekologicheskim zadacham; per. s angl. / F.S. Roberts. — M.: Nauka, 1986. — 496 s.

Zgurovskij M.Z. Printsipy i metody upravlenija impul'snymi protsessami v kognitivnyh kartah slozhnyh sistem / M.Z. Zgurovskij, V.D. Romanenko, Ju.L. Miljavskij // Problemy upravlenija i informatiki. — 2016. — Ch. 1, № 2. — S. 21–29.

Zgurovskij M.Z. Printsipy i metody upravlenija impul'snymi protsessami v kognitivnyh kartah slozhnyh sistem / M.Z. Zgurovskij, V.D. Romanenko, Ju.L. Miljavskij // Problemy upravlenija i informatiki. — 2016. — Ch. 2, № 4. — S. 7–17.

Romanenko V.D. Sintez sledjaschej sistemy upravlenija neustojchivymi impul'snymi protsessami v ierarhicheskih kognitivnyh kartah slozhnyh sistem / V.D. Romanenko, Ju.L. Miljavskij // Systemni doslidzhennja ta informatsijni tekhnolohiyi. — 2016. — № 4. — S. 7–13.

Romanenko V.D. Avtomatizatsija upravlenija impul'snymi protsessami v kognitivnyh kartah s podavleniem ogranichennyh vozmuschenij na osnove metoda invariantnyh ellipsoidov / V.D. Romanenko, Ju.L. Miljavskij // Systemni doslidzhennja ta informatsijni tekhnolohiyi. — 2017. — № 2. s— S. 29–40.

Metody robastnogo, nejro-nechetkogo i adaptivnogo upravlenija: ucheb. / Pod red. N.D. Egupova. — 2-e izd. — M.: Izd-vo MGTU im. Baumana, 2002. — 744 s.

Toivonen H. Lecture notes on robust control by state-space methods. — Available at: users.abo.fi/htoivone/courses/robust/hsem.pdf

Glover K. State-space formulae for all stabilizing controllers that satisfy an H∞ norm bound and relations to risk sensitivity / K. Glover, J.C. Doyle // Systems & Control Letters. — 1988. — Vol. 11, N 8. — P.167–172.

Doyle J.C. State-space solutions to standard and control problems / J.C. Doyle, K. Glover, P. Khargonekar, B. Francis // IEEE Transactions on Automatic Control. — 1989. — Vol. 34, N 8. — P. 831–847.

Safonov M.G. Simplifying the H∞ Theory via Loop Shifting, Matrix Pencil and Descriptor Concepts / M.G. Safonov, D.J.N. Limebeer, R.Y. Chiang // Int. J. Contr. — 1989. — Vol. 50, N 6. — P. 2467–2488.

Iglesias P.A. State-Space Approach to Discrete-Time H∞ Control / P. A. Iglesias, K. Glover // Int. J. Control, 54. — 1991. — P. 1031–1073.

Stoorvogel A.A. The H∞ Control Problem: A State Space Approach / A.A. Stoorvogel. — Prentice-Hall, Englewood Cliffs, 2000. — 275 p.

Robust Control Toolbox. Documentation. Function hinfsyn. — Available at: https://www.mathworks.com/help/robust/ref/hinfsyn.html

Published

2017-12-15

Issue

Section

Mathematical methods, models, problems and technologies for complex systems research