Geometrical Framework Application Directions in Identification Systems. Review

The approaches review of the framework application in identification problems is fulfilled. It is showed that this concept can have different interpretations of identification problems. In particular, the framework is understood as a frame, structure, system, platform, concept, and basis. Two directions of this concept application are allocated: 1) the framework integrating the number of methods, approaches or procedures; b) the mapping describing in the generalized view processes and properties in a system. We give the review of approaches that are the basis of the second direction. They are based on the analysis of virtual geometric structures. These mappings (frameworks) differ in the theory of chaos, accidents, and the qualitative theory of dynamic systems. Introduced mappings (frameworks) are not set a priori, and they are determined based of the experimental data processing. The main directions analysis of geometrical frameworks application is fulfilled in structural identification problems of systems. The review includes following directions: i) structural identification of nonlinear systems; ii) an estimation of Lyapunov exponents; iii) structural identifiability of nonlinear systems; iv) the system structure choice with lag variables; v) system attractor reconstruction.