In the thesis the system approach to a problem of dynamic decision - making in the complex systems described by models of impulse processes in cognitive maps is suggested. Cognitive maps are a popular and convenient tool for describing, modelling, and analyzing complex multidimensional multiconnected systems of different origin. From a mathematical point of view, a cognitive map is a weighted directed graph, the nodes of which represent the main components (concepts) of a complex system, and the edges are the relationships between them. The dynamics of a complex system described by a cognitive map can be represented as a so-called impulse process, which (in the form of Roberts) is a first-order vector difference equation. To date, many studies are known on the construction and analysis of cognitive maps, but there is almost no work that would systematically address the problems of identification (evaluation) and control of systems represented by cognitive maps.
Here the principles, approaches and methods of identification and control of these systems based on the application and adaptation of methods of the theory of system identification and the theory of automatic control are developed. In this case, test signals or controls are fed directly to some nodes of the cognitive map, or, in case of insufficiency of such nodes, the variable weights of the map edges can act as controls. In the case when the number of nodes and /or weight coefficients of the cognitive map edges are unknown, methods for dimension identification and parametric identification of systems based on data from the measured cognitive map nodes are proposed, with measurement errors considered. To stabilize the unstable cognitive map, a number of methods are proposed based on the methods of modal control and control using reference models; other methods are suggested to set the nodes coordinates of the cognitive map to a given level. Cases of multirate impulse process in the cognitive map, of the presence of unmeasured constrained disturbances of arbitrary nature, of the presence of delays, of the need to control the ratios etc. are considered separately.
For control of complex systems, the dynamics of which is presented in the form of impulse processes in cognitive maps, in this thesis the adaptation of methods of the automatic control theory is suggested. The dynamics of the controlled system is written by introducing a control vector that acts directly on the nodes of the cognitive map through the variation of its resources. In simpler cases, it is recommended to use methods based on reference models (if you can vary all nodes) or modal control. Also in the case of stable impulse processes, methods based on minimizing the quadratic optimality criterion can be used. But controls by varying the resources of cognitive map nodes may not be sufficient, because in practice there are often few nodes that a decision maker can actually vary. For this case, the paper first proposes a method of control by varying the weights of the edges of the cognitive map, i.e., essentially by changing the degree of influence of some nodes on others. Then the control vector is the vector of increments of weights of some edges of the cognitive map. The design of a discrete controller for such a controlled impulse process is based on the quadratic optimality criterion for this vector. We also consider the case when a decision maker can use both types of control, i.e. variation of nodes resources, and the degree of their influence on each other. For this purpose the method of combined control is developed.
Particular attention is paid to the disclosure of uncertainties that arise in the presence of unmeasurable disturbances of arbitrary nature, acting on the coordinates of the nodes of the cognitive map. These can be both external perturbations (including the influence of unmeasured nodes) and internal perturbations caused by inaccurate identification or time-varying weights of the map edges. It is assumed that nothing is known about these disturbances, except that they are limited. From the control theory point of view, this is the problem of robust control. In this research, two methods of robust control of impulse processes of the cognitive map are developed and investigated - on the basis of the method of invariant ellipsoids and on the basis of the H-infinity theory.
The practical significance of the obtained results is illustrated by numerous examples of cognitive maps of real systems - an IT company, its human resources department, a commercial bank, a cryptocurrency market, a socio-educational student’s process. The results have been implemented by the IT company “Noosphere”, by the Department of dynamic systems control of Space Research Institute of NASU, in the educational process of Igor Sikorsky KPI and can be used in the future for many complex systems represented by cognitive maps.
