ბესარიონ შანშიაშვილი

Рассматривается задача структурной идентификации нелинейных стационарных систем на множестве непрерывных блочно-ориентированных моделей. Представлены методы структурной идентификации в установившемся режиме при входных периодических воздействиях, имеющих равномерно и абсолютно сходящиеся ряды Фурье, и при входных стационарных случайных процессах с нормальным распределением. По разработанным критериям идентификации структуры модели возможно выделение определенных подмножеств множества моделей для представления структуры модели исследуемой системы.

Рассматривается задача структурной идентификации нелинейных стационарных систем на множестве непрерывных блочно-ориентированных моделей. Представлены методы структурной идентификации в установившемся режиме при входных периодических воздействиях, имеющих равномерно и абсолютно сходящиеся ряды Фурье, и при входных стационарных случайных процессах с нормальным распределением. По разработанным критериям идентификации структуры модели возможно выделение определенных подмножеств множества моделей для представления структуры модели исследуемой системы.

Рассматривается задача параметрической идентификации линейных динамических систем с переменными параметрами. Задача параметрической идентификации ставится как в определенном смысле обратная задача задачи Коши для линейных обыкновенных дифференциальных уравнений. При некоторых ограничениях на параметры, и входные и выходные переменные системы сформулирована и доказана теорема существования такого интервала, где непрерывная матрица коэффициентов идентифицируема. Алгоритм оценивания параметров, а также вопрос подтверждения модели исследованы на примере идентификации системы второго порядка.

Исследуется поведение бинарных систем управления линейными конечномерными динамическими процессами в условиях помех. Полученные результаты позволяют оценить влияние ограниченных помех на динамику управляемых процессов и осуществить синтез бинарных систем управления при наличии неконтролируемых шумов в информации о регулируемых координатах процесса.

Рассматриваются задачи структурной и параметрической идентификации нелинейных стационарных систем при входных синусодальных функциях системы на множестве непрерывных блочно-ориентированных моделей. Разработан критерий определения структуры модели на основе использования численного гармонического анализа. Задача параметрической идентификации, которая непосредственно связана с задачей структурной идентификации, сводится, с помощью численного гармонического анализа и аппроксимации Фурье, к решению систем алгебраических уравнений.

Рассматриваются задачи структурной и параметрической идентификации нелинейных систем с положительной обратной связью на множестве непрерывных блочно-ориентированных моделей с обратной связью. Представлены методы структурной идентификации в установившемся и переходных режимах на основании наблюдений над входными и выходными переменными системы при входных периодических и синусоидальных воздействиях. Решение задачи параметрической идентификации, которую можно непосредственно связать с задачей структурной идентификации, осуществляется также в установившемся и переходных режимах по методу найменьших квадратов.

Рассматриваются задачи структурной и параметрической идентификации нелинейных систем на множестве непрерывных блочно-ориентированных моделей при входных синусоидальных воздействиях системы. Нелинейное статическое звено, входящее в состав блочно-ориентированных моделей, описывается полиномиальной функцией n-й степени, а линейные динамические звенья – устойчивы. Разработан критерий определения структуры модели. Для систем второго порядка решение задачи параметрической идентификации, которая непосредственно связана с задачей структурной идентификации с использованием выражений и экспериментальных данных, полученных для последней, сводится к решению систем алгебраических уравнений.

Рассматривается задача параметрической идентификации одномерных линейных динамических систем с переменными параметрами. Задача параметрической идентификации ставится как в определенном смысле обратная задача задачи Коши для линейных обыкновенных дифференциальных уравнений. При некоторых ограничениях на входные и выходные переменные системы сформулирована и доказана теорема существования такого интервала, где непрерывные параметры системы идентифицируемы. Алгоритм оценивания параметров, а также вопрос подтверждения модели исследованы на примерах идентифика¬ции систем второго порядка как аналитически, так и с помощью компьютерного моделирования.

Рассматривается задача параметрической идентификации линейных динамических систем с переменными параметрами. Задача параметрической идентификации ставится как в определенном смысле обратная задача задачи Коши для линейных обыкновенных дифференциальных уравнений. При некоторых ограничениях на параметры, и входные и выходные переменные системы сформулирована и доказана теорема существования такого интервала, где непрерывная матрица коэффициентов идентифицируема. Алгоритм оценивания параметров, а также вопрос подтверждения модели исследованы на примере идентификации системы второго порядка. на примерах идентифика¬ции двумерных систем как аналитически, так и с помощью компьютерного моделирования.

Рассматриваются задачи структурной и параметрической идентификации нелинейных систем на множестве непрерывных блочно-ориентированных моделей при входных синусоидальных воздействиях системы. Нелинейное статическое звено, входящее в состав блочно-ориентированных моделей, описывается полиномиальной функцией n-й степени, а линейные динамические звенья – устойчивы. Разработан критерий определения структуры модели. Задача параметрической идентификации, которая непосредственно связана с задачей структурной идентификации, с помощью аппроксимации Фурье сводится к решению систем алгебраических уравнений.

Nonlinear dynamical systems with a closed cycle are widely spread in chemical, oil industry, mining and metallurgical industries, in the production of cellulose-paper and cement, in ecology and other areas. Structural and parametrical identification of nonlinear dynamical systems with a closed cycle, with the system’s input determinate functions on the set of continuous-time block-oriented models with feedback is considered. The problem of structural identification in state and transient state is considered. This problem is set issuing from the classical definition by L.Zadeh – the classes of the input signals and of the models are known and design of the model determination criterion from the class is needed. The problem of parametric identification considered issuing from harmonic analysis, Fourier approximation, numerical differentiation, least squares methods. 

Problems of identification of non-linear continuous control systems are considered. Methods for the structural and parametric identification of nonlinear systems on a set of continuous block-oriented models, the elements of which are different modifications of the Wiener and Hammerstein models, are presented. Criteria for determining the structure of a model from the set of models have been developed. The problem of parameter estimation is reduced to solving systems of algebraic equations.

Content of the solute oxygen in some sections or in a particular place of the flow, shortage of the solute oxygen or its biological demand often characterize water quality in the flows. Concentration of the solute oxygen in water is the general index of the pollution (if it is not a toxic poisoning), but there exists a lot of variables which may directly or indirectly influence it. In the given work adapted algorithm of nonlinear systems’ static model structure and of the parameter identification is used for construction of the linear and nonlinear static models of solute oxygen. The solution about the choice of the ‘’best’’ model structure is made not only on the multiple correlation coefficient and the analysis of regression coefficients by the t-criterion. At the model’s “best” structure the estimation of parameters is done using least squares method.

In the given work the problems of structural and parametric identification of the nonlinear systems with positive feedback on the set of block-oriented models with the feedback are considered. The problem of structural identification is posed as follows: classes of models and input signals are given; it is required to develop a criterion identifying the model structures from the class of models. The method of parametric identification, which allows to determine two types of parameters - static characteristics in the steady state, and dynamic characteristics in the transitive state on the basis of the least squares method is offered. 

One of the most essential parameters of any optimal system is the time of finding an extremum, especially if the exact kind of optimized functional and the functions that set constraints, is not known in advance and there is no biunique correspondence between its values and controlled variables. These circumstances have led to the necessity of development new schemes of automatic optimizers. In the work one of them is considered, in which, the value of optimizable variables approaches an extremum with enough high speed without a reverser of effector. Increase in the speed of the automatic optimizer allows reducing the time of search of an extremum.

The problems of structural and parametric identification of nonlinear systems on the set of continuous block-oriented models under the system’s input sinusoidal influences are considered. The problem of structural identification is put according to the classical definition of identification of L.Zadeh. The criterion of determination of the model structure is developed. The solution of parametrical identification problem is reduced to the solution of algebraic equations’ systems. Because of an opportunity of use of the same experimental data, it is possible to do parallel computations according to the developed algorithms of structural and parametrical identification that allows reducing duration of model construction process.

The problems of structural and parametric identification of nonlinear systems on the set of continuous block-oriented models, elements of which are: various modifications of Wiener and Hammerstein models, at the system’s input sinusoidal influences are considered. The problem of structural identification is put according to the classical definition of identification of L.Zadeh. On the basis of application of the numerical harmonious analysis the definition criterion of model structure on the set of models is developed. The problem of the parametric identification of the second order nonlinear systems is considered at their representation by the simple and generalized Hammerstein and Wiener models. Estimations of parameters are obtained by the least squares method.

Structural and parametric identification of the nonlinear systems with a closed cycle on the set of continuous block-oriented models with feedback is considered. The method of the structural identification in the steady state based on the observation of the system's input and output variables at the input periodic influences is proposed. The solution of the parameter identification problems, which can be immediately connected with the structural identification problem, is carried out in the steady and transient states by the method of least squares. The structural and parametric identification algorithms are investigated by means of both the theoretical analysis and the computer modelling.

The problems of structural and parametric identification of nonlinear systems on the set of continuous block-oriented models, elements of which are different modification of Hammerstein and Wiener models, at the system’s deterministic input influences are considered. The problem of the structural identification is considered according to the classical definition of identification of Zadeh. The structure definition criterion of the model is developed. Parameters’ estimations are received by the method of the least squares by using Fourier approximation.

In this article problems of mathematical and computer modeling of adaptive systems identification and control in the class of Wiener-Hammerstein models nonlinear stochastic dynamic power objects are considered. The problem of identification is reduced to minimization of criterion of quality identification on parameters where the optimal two-stage recurrent algorithm of identification - on the basis of the average method of the least squares is applied. The model of Wiener-Hammerstein constructed in this way is applied in the closed contour of identification and control.

The problem of structural identification of nonlinear dynamical systems on a set of continuous block-oriented models with input periodic actions having uniformly and absolutely convergent Fourier series and with input harmonic actions is considered. The problem of structural identification is posed on the basis of the classical definition of Zadeh's identification. Criteria for determining the structure of the model have been developed. Questions of the reliability of the obtained results are investigated.

The problem of parameter identification of linear non-stationary dynamical systems is considered. Stated is the problem of parameter identification as, in a certain sense, an inverse problem of Cauchy’s problem for linear ordinary differential equations with variable coefficients. Under some restrictions on the system’s parameters, and input and output variables the existence theorem of such interval, in which a continuous matrix of coefficients is identified, is formulated and proved. The parameter estimation algorithm, and also the question of the model validation are investigated on the example of the second order system identification.

Structural and parametric identification of the nonlinear continuous dynamic systems with a closed cycle on the set of continuous block-oriented models with feedback is considered. 

Models of systems with closed cycle, taking into account the peculiarities of their operation, are described by the ordinary nonlinear differential equations – Riccati and Duffing equations. Input signals are periodic functions, having absolutely and uniformly convergence trigonometrical series.  

The method of the structural identification in the steady state based on the observation of the system's input and output variables at the input periodic influences is proposed. According to the system stability conditions and Diulak criterion, for the solution of Riccati and Duffig equations, corresponding to the models, it is possible to use the method of a small parameter. On the basis of application of the numerical harmonious analysis the definition criterion of model structure on the set of models is developed.

The solution of the parameter identification problems, which can be immediately connected with the structural identification problem, is carried out in the steady and transient states by the method of least squares. 

The problem of parameter identification of linear non-stationary dynamical systems is consid-ered. It is supposed that direct observation of the state vector of system is not possible and elements of the output matrix are variables. Stated is the problem of parameter identification as, in a certain sense, an inverse problem of Cauchy’s problem for linear ordinary differential equations. Under some restrictions on the system’s parameters, and input and output variables the existence theorem of such interval, in which a continuous matrix of coefficients is identified, is formulated and proved. The parameter estimation algorithm, and also the question of the model validation are investigated on the example of the second order system identification.

Structure and parameter identification of the nonlinear systems with positive feedback on the set of continuous block-oriented models with feedback is considered. The method of the structure identification in the steady state based on the observation of the system's input and output variables at the input periodic influences is proposed. The solution of the parameter identification problems is carried out in the steady and transient states by the least squares method. The structure and parameter identification algorithms are investigated by means of both the theoretical analysis and the computer modeling. According to the proposed identification method the model of the ball-tube mill of the concentrating factory, working in a closed cycle with the classifier, has been determined.

A problem of structure identification of continuous nonlinear dynamical systems on the set of continuous block-oriented models is considered. Methods of structure identification in steady state based on the observation of the system's input and output variables at the input sinusoidal influences, at the input periodical influences, having Fourier's uniformly and absolutely convergent series, and at the input random processes with normal distribution are proposed. The criteria determining the model structure are developed. The structure identification methods are investigated by means of both the theoretical analysis and the computer modelling.

The problem of parameter identification of linear dynamic systems with variable parameters is considered. Stated is the problem of parameter identification as, in a certain sense, an inverse problem of Cauchy’s problem for ordinary differential equations with variable coefficients. Under some restrictions on the system’s parameters, and input and output variables the existence theorem of such interval, in which a continuous matrix of coefficients is identified, is formulated and proved. The parameter estimation algorithm, and also the question of the model validation are investigated on the example of the second order system identification.

The problem of parameter identification of nonlinear dynamic systems of industrial processes on the set of continuous block-oriented models, the elements of which are different modifications of the Hammerstein and Wiener models, is considered. Method of parameter identification in steady state based on the observation of the system's input and output variables at the input sinusoidal influences is proposed. The solution of the problem of parameter identification is reduced to the solution of the systems of algebraic equations by using the Fourier approximation. The parameters’ estimations are received by the least squares method. Reliability of the received results, at the parameter identification of the nonlinear system in industrial conditions at the presence of noise depends on the accuracy of the measurement of system output signals and mathematical processing of the experimental data at the approximation.

A problem of parameter identification of nonlinear dynamic systems of manufacturing processes on the set of block-oriented models in the frequency domain is considered. Method of parameter identification in steady state at the input sinusoidal influences is proposed. The solution of the problem of parameter identification is reduced to the solution of the systems of algebraic equations by using the Fourier approximation. The parameters estimations are received by the least squares method. The identification method is investigated by theoretical analysis and computer modelling.

Structure and parameter identification of nonlinear dynamic systems in the frequency domain on the subset of continuous block-oriented models, elements of which are simple, generalized and expanded Wiener models is considered. Method of structure identification in steady state based on the observation of the system's input and output variables is proposed. The solution of the problem of parameter identification is reduced to the solution of the systems of algebraic equations by using the Fourier approximation. The parameters estimations are received by the least squares method. The identification methods are investigated on accuracy.

A problem of parameter identification of nonlinear manufacturing systems represented by expanded Wiener model, linear elements of which are described by the ordinary differential equation, in the frequency domain is considered. Method of parameter identification in steady state based on the observation of the system's input and output variables at the input harmonic influences is proposed. The solution of the problem of parameter identification is reduced to the solution of the systems of algebraic equations by using the Fourier approximation. The parameters estimations are received by the least squares method. Reliability of the received results, at the identification of the nonlinear systems in industrial conditions at the presence of noise, depends on the accuracy of the measurement of system input and output signals and mathematical processing of the experimental data at the approximation. The parameter identification method is investigated by means of both the theoretical analysis and the computer modelling.

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