Systems Theoretic Techniques for Modeling, Control and Decision Support in Complex Dynamic Systems

Nowadays, modern complex systems of any interdisciplinary nature can hardly be analyzed and/or modeled without comprehensive usage of system theoretic approach. The complexity and uncertainty of the nature of modern systems, and the heterogeneity of related information, require a complex approach for their study, based on systems theory and systems analysis and consisting of information and expert knowledge management, initial pre-processing, modeling, simulation, and decision making support. As the complexity of systems increases, system theoretic methods become more crucial. Often they provide the only effective tools of obtaining the information about the elements in a system, connections between those elements, and the means for getting the adequate representation of system in a whole. The variety of complex systems can be described by deterministic or stochastic differential equations, statistical mechanics equations, neural network models, cellular automata, finite state machines, multi-agent systems, etc. Most of the complex real world objects are modeled as dynamic systems enriched by artificial intelligence resources. Equipped with artificial intelligence techniques, these models offer a wide variety of advantages such as coping with incomplete information and uncertainty, predicting system’s behavior, reasoning on qualitative level, knowledge representation and modeling, where computer simulations and information systems play an important and active role, and facilitate the process of decision making.

This chapter aims to discuss the problems of modeling, control, and decision support in complex dynamic systems from a general system theoretic point of view, with special emphasis on methodological aspects. We consider the main characteristics of complex systems and of system approach to complex system study. Then the chapter continues with the general dynamic modeling and simulation technique for complex hierarchical systems functioning in control loop. The proposed technique is based on the information-mathematical models and described in terms of the hierarchical state transition diagrams. The methodology is sufficiently abstract to allow both qualitative and quantitative analysis of system state dynamics and control through hierarchical scenario calculus. The evaluation of different scenarios is defined by the multiple criteria vector-functions related to the efficiency of control strategies and time required for system goals achievement. We also offer general architectural and structural models of computer information system intended for simulation and decision support in complex systems.

Keywords: Modeling, control, decision, complex dynamic systems, complex hierarchical systems.