The presented dissertation thesis deals with the modeling and identification of nonlinear dynamical systems of various dynamics. The thesis presents a theoretical analysis of methods, algorithms, and principles for modeling and identification of nonlinear dynamical systems using classical and intelligent methods. The primary goal of the dissertation thesis is the proposal of a complex methodology for modeling and identification of physical systems of various dynamics using classical methods and methodology based on artificial intelligence methods. The proposed methodology based on classical methods combines analytical and experimental identification methods and is verified within two case studies of modeling and identification of the aerodynamic levitation plant and the helicopter educational model. The proposed methodology of experimental identification using artificial intelligence methods is verified within the third case study on the helicopter educational model. Obtained gray-box models and black-box models of physical systems, which represent digital twins of real physical systems, are used for the design and verification of stabilizing control algorithms using MATLAB / Simulink software tools including application Toolboxes. The thesis illustrates the implementation of models of physical systems forming a research and development platform into the DCS network control system in CMCT&II at the DCAI FEEI TU of Košice. In the thesis, an analysis of the distributed control system of the ALICE experiment at CERN and the modification of DCS software modules developed by the CMCT&II is presented. Software modules were developed by CMCT&II as part of the research project The ALICE experiment on LHC at CERN.