Structural Identification of Nonlinear Dynamic Systems

Abstract

The method of structural identification nonlinear dynamic systems is offered in the conditions of uncertainty. The method of construction the set containing the data about a nonlinear part of system is developed. The concept of identifiability system for a solution of a problem structural identification is introduced. The special class of structures S for a solution of problem identification is introduced. We will show that the system is identified, if the structure S is closed. The method of estimation the class of nonlinear functions on the basis of the analysis sector sets for the offered structure S is described. We showed, as on S a preliminary conclusion about a form of nonlinear function to make. We offer algorithms of structural identification of single-valued and many-valued nonlinearities. Examples of structural identification of nonlinear systems are considered.

Estimation of Spectrum Eigenvalues Dynamic System on the Basis of Application Lyapunov Exponents

“…We will explain a method of solution a problem for system (1) second order [9]. Consider system (1) with one input and an output.…”

“…The idea of application Lyapunov exponents in identification problems is stated in [9], [10]. The offered approach is based on the analysis of coefficient structural properties (CSP) [10].…”

“…We will show at first relationship between CSP and LE. For an estimation of structural properties of this system introduce CSP [9]     …”

“…For identification of the particular solution of system the special class of static models with the dynamic specification on an input is used. For the first time such approach has been offered in [9]. In work we give generalization of this approach for a case of linear dynamic systems.…”

“…For this purpose we form the time series describing a modification LE. For identification SE we introduce special structures [9], [10] for describe of modification LE. We apply a method of secants and we receive the approached estimations of a spectrum.…”