KVT, 2016, Issue 184, pp.44-56
CONTROL METHOD IN COGNITIVE MAPS BASED ON WEIGHTS INCREMENTS
Educational and Scientific Complex “Institute for Applied Systems Analysis” of National Technical University of Ukraine “Kyiv Polytechnic Institute”, Kiev, Ukraine
Introduction. Cognitive maps are widely used for modeling large multidimensional systems. These are weighted oriented graphs that represent concepts and relations between them. When external or internal disturbances affect the system impulse process is initiated. It is described by first-order equation in increments of vertices coordinates. A number of articles solved a problem of control in cognitive map’s impulse process by means of control theory methods. But all of them used external control inputs, i.e. resources of the vertices, for this purpose.
The purpose of the article is to develop new method of control where cognitive map’s edges weights are used as controls for impulse process stabilisation.
Results. New method of control of cognitive maps was developed. It is based on varying of the map’s edges weights. It was supposed that some of the vertices may affect other ones in different way, i.e. stronger or weaker. After presenting impulse process model in full coordinates weights increments were added to the difference equation. They were considered as control inputs which were generated according to the control law developed based on quadratic criterion. Stability of the closed-loop system was demonstrated. To verify the results, method was simulated using cognitive map of student’s socio-educational process. Finally we obtained that for stable cognitive map vertices’ coordinates are quickly stabilised at new levels via edges’ weights varying.
Conclusion. Applying the proposed method of control based on weights varying to impulse process of cognitive map allows setting vertices coordinates on desired levels.
Keywords: cognitive map, control law, weights increments, stabilisation at new levels.
1 Axelrod R. The Structure of Decision: Cognitive Maps of Political Elites. Princeton University Press, 1976, 404 p.
2 Roberts F. Discrete Mathematical Models with Applications to Social, Biological, and Environmental Problems. Englewood Cliffs, Prentice-Hall, 1976, 559 p.
3 Gorelova G.V., Zakharova E.N., Radchenko S.A. Research of semi-structured problems in socio-economic systems. Cognitive approach. Rostov-na-Donu: Publisher RSU, 2006, 332 p. (in Russian).
4 Romanenko V.D., Milyavskiy Y.L. Stabilizing of impulse processes in cognitive maps based on state-space models. System Research & Information Technologies, 2014, No1, pp. 26–42 (in Russian).
5 Romanenko V.D., Milyavskiy Y.L., Reutov A.A. Adaptive Control Method for Unstable Impulse Processes in Cognitive Maps Based on Reference Models. Journal of Automation and Information Sciences, 2015, No 2 pp. 35–45 (in Russian). https://doi.org/10.1615/JAutomatInfScien.v47.i3.20
6 Romanenko V.D., Milyavskiy Y.L. Coordinates ratio control for cognitive model of a complex system under unstable impulse process. System Research & Information Technologies, 2015, No1, pp. 121–129 (in Russian).
7 Romanenko V.D., Milyavskiy Y.L. Impulse processes stabilisation in cognitive maps of complex systems based on modal state controllers. Kibernetika i vycislitel’naa tehnika, 2015, No179, pp. 43–55 (in Russian).
8 Romanenko V.D., Milyavskiy Y.L. Adaptive coordinating control of interacting cognitive maps vertices’ ratios in impulse mode. System Research & Information Technologies, 2015, No3. pp. 109–120 (in Russian).