ISSUE 179, article 4


Kibern. vyčisl. teh., 2015, Issue 179, pp 43-55.

Romanenko Victor D., Dr (Engineering), Prof., Deputy Director for Scientific and Pedagogical Work, Institute for Applied Systems Analysis of National Technical University of Ukraine “Kiev Polytechnic Institute”, Peremogy Ave. 37, Kiev, 03056, Ukraine, email:

Milyavskiy Yurii L., PhD (Engineering),Assistant of the Department of Mathematical Methods of System Analysis of the Institute for Applied Systems Analysis of National Technical University of Ukraine “Kiev Polytechnic Institute”, Peremogy Ave. 37, Kiev, 03056, Ukraine, email:


Introduction. Cognitive modelling is one of the most widespread approaches for ill-structured socio-economic systems research nowadays. It is usually used when subject of enquiry is a complex high-dimensional system; in fact, most of financial, economical, social, political systems belong to this category. Cognitive map (CM) is a directed graph, where vertices represent concepts, directed edges represent the causal effect relationships between concepts, and the weights of edges represent the degree of the causal effect. When CM switches to transition process as a result of external or internal impulse, so called «impulse process» is described by difference first-order equation for increments. It was previously shown by the authors that impulse process can also be equivalently expressed by state-space model. One of the most important questions is how to stabilise unstable CM. For this purpose control inputs should be added to the system. Then the problem of regulators design arises.

Purpose of the paper is to investigate possibility of applying modal control methods for state regulators design (with single and multiple controls) to stabilise unstable impulse process in CM.

Results. Different methods of modal control were investigated and applied for CM impulse process stabilisation. CM dynamics was presented by state space model. Problem of external control inputs for CM was discussed. It was demonstrated that as opposed to «input — output» models, state space models allow to use smaller number of controls for stabilisation (if the system is controllable). Cases with single and multiple inputs were discussed. Impulse process in the CM for commercial bank was simulated, and different approaches to modal regulators design were applied for this cognitive model. Simulation results demonstrated efficiency of the proposed approach to CM stabilisation. It was also shown that modal control with multiple inputs is preferable where possible because it allows to get quicker response and smoother transition process with lower amplitude of control inputs.

Conclusion. Applying of modal control methods allows effective stabilising of CM. Using multiple control inputs helps to increase performance and make transition process smoother and easier to implement.

Keywords: cognitive map, modal control, impulse process stabilisation, closed loop pole placement.

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Received 30.11.2014