Problems and Methods of Modelling in Complex Large-Scale Systems Dynamics

Abstract

This research is generated by urgent problems of modelling and qualitative analysis in dynamics of complex large-scale systems, with multiple time scales. The methods, elaborating the general conception of the modelling, based on A. M. Lyapunov methods and N. G. Chetayev ideas, are elaborated. The simple schemes of engineering level for decomposition-reduction of original models and dynamic properties are developed; unified view point, formed on basic postulates (stability-singularity) is established. Besides considered objects and problems are treated as singularly perturbed ones (in sense of A. N. Tikhonov, A. Nayfeh, S. Campbell, L. K. Kuzmina). In the engineering applications this approach and obtained results enable to build the optimal decomposed models, known and new ones, by strict mathematical methods, with acceptability substantiation of these models for analysis, control problems. The examples of concrete physical nature are investigated.