The method of structural identification 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) which allows 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 nonlinearities is given.
The procedure of structural identification of hysteresis functions is developed. Procedure realization is based on the phenomenological analysis of structure VS. Defini-tion 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.
Algorithms 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 fragments VS in two planes. Such analysis allows the make a decision about hysteresis structure. We show that the offered methodology is applicable to unstable dynamic systems. Results of the computer simulation are given.

Adaptive algorithms of parametric identifica-tion of discrete systems with lag variables are proposed. Adaptive algorithms (AA) in the presence of lag input variables are developed. The convergence of the AA and the boundedness of the trajectories the adaptive system is proved. Convergence domain АА depends on operating disturbance. Models with multiplicative parameters (MPM) for the decrease of a number estimated parameters are offered. The process for selection of the vector of base parameters MPM was developed. The performance of adaptive system identification for this case is proved. It is shown that parameters of system estimation at the application of multiplicative identification must be chosen from a condition of minimization of the criterion of the prediction error. Transformation of interdependence be-tween the lagged variables is offered, allowing eliminating their effect on system work. In the second part of work, the method of synthesis АА identification of the systems containing lagged output variables is offered. We consider a case of linear correlation between an output of the system and operating disturbance. For a solution of a problem, we suggest fulfilling an estimation of operating disturbance. Corresponding procedures are described and proved their efficiency. Simulation results are presented that confirm the efficiency of the adaptive methods.

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. Defini-tion 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 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 an estimation quality indicators of linear dynamic system in the conditions of uncertainty is considered. Quality indicators are a point of an equilibrium state and a spectrum of eigenvalues. We offer a method of an estimation a point of an equilibrium state. Method is based on identification of the particular solution system on a class of static models with the dynamic specification on an input. We offered on the basis of the general decision of system procedures and criteria of an estimation equilibrium state. After an estimation of equilibrium state system in work the problem of definition a spectrum eigenvalues of linear dynamic system is considered. We form the time series describing a modification of Lyapunov exponents. For identification of a spectrum eigenvalues we introduce special structures which describe a modification of the Lyapunov exponent. We apply a method of the secant structures and we receive spectrum tentative estimations. The special structure, allowing identifying the largest Lyapunov exponent, is offered. Generalization of the offered methods on linear non-stationary dynamic systems is given.

Methods of structural identification of static systems with a vector input and several nonlinearities in the conditions of uncertainty are considered. We consider inputs irregular. The concept of structural space is introduced. In this space special structures (virtual portraits) are analyzed. The Holder condition is applied to construction of sector set, to which belongs a virtual portrait of system of identification. Criteria of decision-making on a class of nonlinear functions on the basis of the analysis of proximity of sector sets are described. Procedures of an estimation of structural parameters of two classes of nonlinearities are stated: power and a hysteresis.

The problem of structural identification of systems with the distributed lag in the conditions of uncertainty is considered. Known statistical approaches are laborious and not always allow making the decision on lag structure. Therefore in work for the problem decision the special class of static structures (SS) (virtual portraits) explored system is introduced. Process of the decision of a problem consists of two steps. At the first step set of secants for initial system is under construction. Completeness of set of secants is a sign of linearity of system. Nonfulfilment of conditions of completeness is a sign of nonlinearity of system. Estimation of nonlinearity of system execute on an indicator of level of nonlinearity of the system, offered in work. At the second step the special structural space is introduced and is defined SS for a nonlinear part of system. The estimation of nonlinear properties of system is executed on the basis of identification of parameters of set of secants SS. Criteria and algorithms of decision-making on structure of a lag on the basis of the analysis of virtual portraits are offered. The analogue of criterion of Durbin-Watson is offered. The received results are generalized on a case of the distributed lag in input and output variables of system. It is shown that to structural identification of systems with the distributed lag we will not apply the analysis of sector sets. The approach to parametrical identification of system with the distributed lag in the conditions of uncertainty is offered.

The approach to an estimation of area of parametrical restrictions (APR) for static linear system on parameters in the conditions of uncertainty is of-fered. For decision-making indicators of domination of an exit of model over an exit of system and the special indicator setting admissible level of errors of domination are used. The case of the representation of area of restrictions in the form of boundaries from below and from above on a modification of parameters of system is considered. The iteration algorithm of identification of restrictions and decision-making is offered. The adaptive algorithm of an estimation of boundaries of area of parametrical restrictions is synthesized. Procedure of estimation APR on the basis of the analysis of a field of secants of system is described. Method development on a case of representation APR in the form of restriction on norm of a modification of parameters of system is given. Various forms of vectorial norms and algorithms of construction of area of parametrical restrictions corresponding to them are considered.