The difficult problem of modeling Complex Dynamic Systems (CDS) is carefully reviewed. Main characteristics of CDS are considered and analyzed. Today’s mathematical models and approaches cannot provide satisfactory answers to the challenging problems of the society. The key problem of complex dynamic systems and control theory consists in the development of methods of qualitative analysis of the dynamics and behavior of such systems and in the construction of efficient control algorithms for their efficient operation. The purpose of control to bring the system to a point of its phase space which corresponds to maximal or minimal value of the chosen efficiency criterion is reviewed and analyzed. The reasons for using Fuzzy Cognitive Maps (FCMs) in modeling Complex dynamic Systems are provided. The basics of FCMs are briefly presented. An illustrative example is considered and interesting results are presented and discusse
