Application of Impulse Process Models with Multirate Sampling in Cognitive Maps of Cryptocurrency for Dynamic Decision Making

Abstract

AbstractIn this chapter a cognitive map (CM) of cryptocurrency application in the financial market is developed, based on which the dynamic model of impulse processes of CM in the form of a system of difference equations (Roberts equations) with multirate sampling is described. The original CM model is decomposed into subsystems with fast- and slow-measured node coordinates. The subsystems are interconnected with each other and are represented with multirate sampling of coordinates. The realization of external control vectors for the subsystem with fast-measured and slow-measured node coordinates by varying some coordinates that can be measured by a decision maker is performed. Closed-loop subsystems of CM impulse process control are implemented, which include multidimensional discrete controllers designed based on the method of invariant ellipsoids. The controllers in the subsystems generate external controls with multirate sampling and affect directly the CM nodes by varying their coordinates. The problem of designing the above discrete-time controllers for suppression of constrained internal and external disturbances is solved. External disturbances include a variety of information disturbances acting on the system. Internal disturbances include changes in the influence of CM nodes on each other, for instance, fluctuations of weight coefficients of CM with respect to their basic values. The basic values are determined by an expert based on cause-effect relations or by the preliminarily identification of the CM model parameters. The mutual influence of interconnected CM subsystems on each other is also taken into account as internal disturbances. The designed control is implemented by a decision maker in the corresponding sections of the CM. By numerical simulation, the efficiency of the designed discrete controllers was investigated and the system performance was compared in the presence and absence of controls.KeywordsCognitive mapMultirate samplingLinear matrix inequalitiesCryptocurrencyState controllerInvariant ellipsoid