Methods of Impulse Processes Control for Cognitive Maps with Delays

Authors

  • Віктор Демидович Романенко Educational and Scientific Complex "Institute for Applied Systems Analysis" of National Technical University of Ukraine “Kyiv Polytechnic Institute” http://orcid.org/0000-0002-6222-3336
  • Юрій Леонідович Мілявський Educational and Scientific Complex "Institute for Applied Systems Analysis" of National Technical University of Ukraine “Kyiv Polytechnic Institute” http://orcid.org/0000-0003-0882-3418

DOI:

https://doi.org/10.20535/1810-0546.2015.5.51376

Keywords:

Cognitive map, Impulse process, System with delays, Control algorithm

Abstract

Background. The paper deals with the problem of cognitive modelling, namely control of complex systems with dynamics in impulse process presented by cognitive maps. It is assumed that the systems operate with delays that may occur either between vertices coordinates of a cognitive map or during transmission of control signals.

Objective. Build models of cognitive maps with different delays and to apply these models to control impulse processes in cognitive maps.

Methods. The article discusses two approaches for delays – control delays and delays during interaction between the vertices of a cognitive map. For the first case, a control algorithm based on reference model of a closed system was proposed, for the second case it is based on quadratic optimality criterion. Obtained results were verified using cognitive maps of commercial bank and health care system. Different delays were included into these systems and control laws were developed.

Results. Simulation results have confirmed that proposed methods reach the objective, i.e. they allow stabilising system with delays in impulse mode.

Conclusions. Research provided in the paper extended the class of controlled cognitive maps by systems with delays.

Author Biographies

Віктор Демидович Романенко, Educational and Scientific Complex "Institute for Applied Systems Analysis" of National Technical University of Ukraine “Kyiv Polytechnic Institute”

Victor Romanenko,

Vice Director of research and education, Dr. Sci, Professor

Юрій Леонідович Мілявський, Educational and Scientific Complex "Institute for Applied Systems Analysis" of National Technical University of Ukraine “Kyiv Polytechnic Institute”

Yuriy Milyavsky,

Senior lecturer at the Department of the mathematical methods of system analysis, Ph.D.

References

F. Roberts, Discrete Mathematical Models with Applications to Social, Biological, and Environmental Problems.Englewood Cliffs, Prentice-Hall, 1976, 559 p.

B. Kosko, “Fuzzy cognitive maps”, Int. J. Man-Machine Stud., vol. 24, pp. 65–75, 1986. Doi: 10.1016/s0020-7373(86)80040-2.

J. Aguilar, “A Survey about fuzzy cognitive maps papers”, Int. J. Computational Cognition, vol. 3, pp. 27–33, 2005.

V. Maksimov, “Structural–target analysis of socio-economic situations development”, Problemy Upravleniya, no. 3, pp. 30– 38, 2005 (in Russian).

Z. Avdeeva et al., “Cognitive approach in control”, Problemy Upravleniya, no. 3, pp. 2–8, 2002 (in Russian).

L. Chun-Me, “Using fuzzy cognitive map for system control”, WSEAS Transactions on Systems, vol. 7, pp. 1504–1515, 2008.

G. Gorelova et al., Research of Semi-Structured Problems in Socio-Economic Systems. Cognitive Approach. Rostov-on-Don, Russia: Izdatelstvo RGU, 2006, 332 p. (in Russian).

M. Hagiwara, “Extended fuzzy cognitive maps”, in Proc. 1st IEEE Int. Conf. Fuzzy Systems, March 8–12,San Diego,CA, 1992, pp. 795–801. Doi: 10.1109/fuzzy.1992.258761.

V. Romanenko and Y. Milyavskiy, “Stabilizing of impulse processes in cognitive maps based on state-space models”, Systemni Doslidzhennya ta Inform. Technologiyi, no. 1, pp. 26–42, 2014 (in Russian).

V. Romanenko et al., “Adaptive control method for unstable impulse processes in cognitive maps based on reference models”, Problemy Informatiki i Upravleniya, no. 2, pp. 35–45, 2015 (in Russian).

V. Romanenko and Y. Milyavskiy, “Coordinates ratio control for cognitive model of a complex system under unstable impulse process”, Systemni Doslidzhennya ta Inform. Technologiyi, no. 1, pp. 121–129, 2015 (in Russian).

W. Zhang and S. Chen, “A logical architecture for cognitive maps”, in Proc. 2nd Int. Conf. Neural Networks, vol. 1, Boumemouth, UK, 1988, pp. 231–238. Doi: 10.1109/icnn.1988.23852.

R. Isermann, Digital Control Systems. Springer-Verlag, 1981, 566 p. Doi: 10.1007/978-3-662-02319-8.

Published

2015-11-02

Issue

Section

Art