I.J. Intelligent Systems and Applications, 2016, 7, 1-13 Published Online July 2016 in MECS (http://www.mecs-press.org/) DOI: 10.5815/ijisa.2016.07.01 Copyright © 2016 MECS I.J. Intelligent Systems and Applications, 2016, 7, 1-13 Structural Identification of Dynamic Systems with Hysteresis Nikolay Karabutov Dept. of Problems Control, Moscow technological University (MIREA), Moscow, Russia E-mail: kn22@yandex.ru, nik.karabutov@gmail.com Abstract —The method of structural identification dynam- ic systems with a hysteresis in the conditions of uncer- tainty 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 non- linear dynamic systems is introduced. Structural identifi- ability is a necessary condition of obtaining the original form of hysteresis. The criterion of structural identifiabil- ity is proposed. The solution of a problem selection the class of the functions belonging to hysteresis to nonline- arities 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 hys- teresis 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 appli- cable to unstable dynamic systems. Results of the com- puter simulation are given. Index Terms—Structural identification, structure, secant, framework, coefficient of structural properties system, structurally-frequency method hysteresis. I. INT RODUCT ION The problem of structural identification occupies one of the basic places in control theory. In the theory of par- ametric identification considerable results are received. Research in the domain of structural identification de- mands the further advancing. The problem has not ob- tained the final decision. Such condition of the problem structural identification (SI) explains complexity of mathematical statement the problem and lack of regular methods of its solution. The majority of approaches to SI are grounded on search of models from the give set or approximation of a nonlinear part system on the class of polynomials. The basis of the specified approaches is parametric identification. Methods of an estimation structure are widely applied to the systems described by integral equations of Wiener and Wiener-Hammerstein. In [1] structure of model is set a priori. Nonlinearity is described by polynomial function of the second order. Basic virtues of Wiener and Wiener- Hammerstein models: (i) transformation of models to the regression form; (ii) application of parametric methods identification for their construction. Application Wiener and Wiener-Hammerstein models is given in [2]. Authors consider the a priori information on nonlinearity frame- work. The piecewise-linear approximation is applied to the nonlinearity description. Different approaches to iden- tification of nonlinear plants on the basis of Wiener and Wiener-Hammerstein models are considered in [3, 4]. In the review [5] is given the analysis of the condition problem identification nonlinear processes in structural dynamics. Many nonlinear processes in a structural dy- namics are described by the equations with a hysteresis. Time and frequency methods of parametric identification are considered. Methods of an estimation of type nonline- arity are analyzed. Different physical and frequency methods, and procedures for handling results of an exper- iment are used for the construction of parametric models. Typical methods, applicable for studied subject domain, are considered in review. Methods of the correlation analysis [6] and error localization in a linear model updat- ing framework [7, 8], and also pattern recognitions [9] were applied to an estimation of type nonlinearity. The problem of an estimation of type nonlinearity solves on the class of the specified models. The problem of a choice the dependence describing nonlinearity is considered. Application of polynomial approximation the initial stage in the presence of the a priori information is justified. The choice of the order polynomial is the main problem of this approach. Criteria and algorithms of an estimation of an order polynomial are considered. They are based on the calculation of the significance factor [10] and the co- herence function [11]. Shortages of such approach are noted. The models received by means of these approaches, not always adequately describe examined processes. In [12] Bayesian approach is applied to the estimation of the polynomial order. In [5] limitation of the polynomial ap- proach is noted. Models does not allow describing the wide class of nonlinearities.