The method of structural identificat ion dynamic systems with a hysteresis in the conditions of uncertainty is developed. The method is based on selection of the special set containing the information on properties of a nonlinear part system. The virtual structure (VS) wh ich allo ws the make the decision about hysteresis structure is offered. The concept of structural identifiability of nonlinear dynamic systems is introduced. Structural identifiability is a necessary condition of obtaining the original form of hysteresis. The criterion of structural identifiability is proposed. The solution of a problem selection the class of the functions belonging to hysteresis to nonlin earities is given. The procedure of structural identification of hysteresis functions is developed. Procedure realization is based on the phenomenological analysis of structure VS. Defin ition of features and properties of the VS is the goal of phenomenological analysis. Each non-linearity introduces the features in the behavior of the system. Therefore, their detection gives only the concrete analysis of VS. Algorith ms of estimation structural parameters the hysteresis in the conditions of uncertainty are offered. They analyze the data in special structural space and are based on the application of secant method VS. Such approach gives adequate estimations of parameters hysteresis. The method of the structurally-frequency analysis is offered for check of the obtained results and estimations. It is based on the analysis of frag ments VS in t wo planes. Such analysis allows the ma ke a decision about hysteresis structure. We show that the offered methodology is applicable to unstable dynamic systems. Results of the computer simulation are given.

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.

The problem of structural identification linear dynamic systems on the basis of the analysis Lyapunov exponent in the conditions of uncertainty is considered. The method of estimation the general solution system on the basis of application static model is developed. Definition of Lyapunov exponent (LE) on the analysis of a coefficient structural properties system is grounded. On the basis of a coefficient of structural properties the special structures reflecting change LE are introduced. The criterion of estimation an order system on the basis of the analysis behaviour these structures are offered. The decision-making method about type of roots dynamic system on the basis of the analysis of time series and the structures reflecting change LE is developed. Two approaches to an estimation of the largest LE and the Perron bottom indexes are offered. The first approach to identification of a change in a coefficient of structural properties with the help secant method for various classes of roots is grounded. The second approach is the structurally-frequency method grounded on definition of estimations LE by means of the analysis of local minima of structures offered in work. The frequency method which is a modification of a method a bar graph in the statistical theory is applied to a validation of the obtained estimations. Results of simulation confirm effectiveness of the offered methods, structures and procedures.

The new approach to structural identification of nonlinear dynamic systems under uncertainty is proposed. It is based on the analysis of virtual frameworks (VF), reflecting a state of a nonlinear part system. Construction VF is based on obtaining special an informational set describing a steady state of a nonlinear dynamic

Objectives. The solution to the relevant problem of identifying systems with multiple nonlinearities depends on such factors as feedback, ways of connecting nonlinear links, and signal properties. The specifics of nonlinear systems affect control systems design methods. As a rule, the basis for the development of a mathematical model involves the linearization of a system. Under conditions of uncertainty, the identification problem becomes even more relevant. Therefore, the present work sets out to develop an approach to the identification of nonlinear dynamical systems under conditions of uncertainty. In order to obtain a solution to the problem, an adaptive identification method is developed by decomposing the system into subsystems.Methods. Methods applied include the adaptive identification method, implicit identified representation, S-synchronization of a nonlinear system, and the Lyapunov vector function method.Results. A generalization of the excitation constancy condition based on fulfilling the S-synchronizability for a nonlinear system is proposed along with a method for decomposing the system in the output space. Adaptive algorithms are obtained on the basis of the second Lyapunov method. The boundedness of the adaptive system trajectories in parametric and coordinate spaces is demonstrated. Approaches for self-oscillation generation and nonlinear correction of a nonlinear system are considered along with obtained exponential stability conditions for the adaptive system.Conclusions. Simulation results confirm the possibility of applying the proposed approach to solving the problems of adaptive identification while taking the estimation of the structural identifiability (S-synchronization) of the system nonlinear part into account. The influence of the structure and relations of the system on the quality of the obtained parametric estimates is investigated. The proposed methods can be used in developing identification and control systems for complex dynamic systems.