THE PROBLEM OF CHOOSING A DUMPING FACTOR IN THE EFFECTIVE CONTROL MODEL FOR DIRECTED WEIGHTED SIGNED GRAPHS
Abstract
The paper deals with the problem of choosing a dumping factor in the effective control model based on maximizing the transfer of impacts for fuzzy cognitive models represented by directed weighted signed graphs. To transfer influence, a management model is used that implements the development of the system. An effective control algorithm is based on solving the optimization problem of finding a vector of external influences that maximizes the accumulated increase in increments of vertex indicators. The optimal control effect is considered to be a control that provides the maximum ratio of the square of the norm of the response vector of the system to the square of the norm of the control vector. The dumping factor of this model controls the comparative scale of the direct and indirect influence of all intrafactor relationships of the system as a whole. The purpose of the study is to determine such areas of acceptable values for the obtained solutions, in which (i) the condition of consistency of the result is met; (ii) the change of vertex ranks is slow. By the sequence of results, we mean satisfaction with the rules of the system as a whole. These rules can be expressed in imposing restrictions on the status of vertices, on the sign of impacts and responses. Set the damping factor, called the resonance, where resonance occurs a surge in the value of the objective function the problem of maximization of the impact when there is no alignment between the resonant response and caused its effect. The choice of the dumping factor affects the value of the target function of the impact maximization problem and the vector of effective management on which this solution is achieved. The value of the resonant damping coefficient can be interpreted as the limit of the possible controllability of the system, i.e. limit the potential impact on the system without harming it. The proposed solution is evaluated based on the degree of stability of the rank of model nodes depending on the influence of changes in the damping coefficient, the algorithmization of determining the range of its acceptable values and the shape of the resonance within the values of the damping coefficient.
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