CONSTRUCTION OF INTEGRAL MODELS FOR NON-LINEAR DYNAMIC SYSTEMS BY MEANS OF VOLTERRA SERIES

The aim is to solve the problem on the restoration of the non-symmetric multidimensional Volterra nuclei, to construct the computer procedures and to realize them as a program-computer complex. The 1-st kind two- and three-dimenstional integral Volterra equations to which the identification problem of the non-symmetric Volterra nuclei has been reduced in case of the special test distorptions have been deduced and investigated. The difference analogs of the obvious conversion formulat in these equations have been obtained. The resistance of the numerical solution to the errors of the initial data has been investigated. The software which have been approved both on the series of test problems and for constructing mathematical model of the real heat-physical process have been createdAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio

On the Optimal Control Problem for Vibrations of the Rod/String Consisting of Two Non-Homogeneous Sections with the Condition at an Intermediate Time

We consider an optimal boundary control problem for a one-dimensional wave equation consisting of two non-homogenous segments with piecewise constant characteristics. The wave equation describes the longitudinal vibrations of a non-homogeneous rod or the transverse vibrations of a non-homogeneous string with given initial, intermediate, and final conditions. We assume that wave travel time for each of the sections is the same. The control is carried out by shifting one end with the other end fixed. The quality criterion is set on the entire time interval. A constructive approach to building an optimal boundary control is proposed. The results obtained are illustrated with an analytical example

Integral Equations Related to Volterra Series and Inverse Problems: Elements of Theory and Applications in Heat Power Engineering

The paper considers two types of Volterra integral equations of the first kind, arising in the study of inverse problems of the dynamics of controlled heat power systems. The main focus of the work is aimed at studying the specifics of the classes of Volterra equations of the first kind that arise when describing nonlinear dynamics using the apparatus of Volterra integro-power series. The subject area of the research is represented by a simulation model of a heat exchange unit element, which describes the change in enthalpy with arbitrary changes in fluid flow and heat supply. The numerical results of solving the problem of identification of transient characteristics are presented. They illustrate the fundamental importance of practical recommendations based on sufficient conditions for the solvability of linear multidimensional Volterra equations of the first kind. A new class of nonlinear systems of integro-algebraic equations of the first kind, related to the problem of automatic control of technical objects with vector inputs and outputs, is distinguished. For such systems, sufficient conditions are given for the existence of a unique, sufficiently smooth solution. A review of the literature on these problem types is given

Integral Models in the Form of Volterra Polynomials and Continued Fractions in the Problem of Identifying Input Signals

The paper discusses the prospect of using a combined model based on finite segments (polynomials) of the Volterra integral power series. We consider a case when the problem of identifying the Volterra kernels is solved. The predictive properties of the classic Volterra polynomial are improved by adding a linear part in the form of an equivalent continued fraction. This technique allows us to distinguish an additional parameter—the connection coefficient α, which is effective in adapting the constructed integral model to changes in technical parameters at the input of a dynamic system. In addition, this technique allows us to take into account the case of perturbing the kernel of the linear term of the Volterra polynomial in the metric C[0,T] by a given value δ, implying the ideas of Volterra regularizing procedures. The problem of choosing the connection coefficient is solved using a special extremal problem. The developed algorithms are used to solve the problem of identifying input signals of test dynamic systems, among which, in addition to mathematical ones, thermal power engineering devices are used

Integral Models Based on Volterra Equations with Prehistory and Their Applications in Energy

The paper addresses the application of Volterra integral equations of the first kind for modeling dynamic power systems. We study the problem of forecasting the commissioning of capacities of the electric power system, taking into account various hypotheses about the dynamics of equipment aging, and the known prehistory. The numerical results of the application of two models to the problem of the development of a large electric power system using the example of the Unified Energy System of Russia are presented. Theoretical results were formulated for a two-dimensional Volterra integral equation of the first kind with variable limits of integration. This class of equations arises when solving the actual problem of identifying variable characteristics of a nonlinear dynamic system of the “input-output” type

Identification of Quadratic Volterra Polynomials in the “Input–Output” Models of Nonlinear Systems

In this paper, we propose a new algorithm for constructing an integral model of a nonlinear dynamic system of the “input–output” type in the form of a quadratic segment of the Volterra integro-power series (polynomial). We consider nonparametric identification of models using physically realizable piecewise linear test signals in the time domain. The advantage of the presented approach is to obtain explicit formulas for calculating the transient responses (Volterra kernels), which determine the unique solution of the Volterra integral equations of the first kind with two variable integration limits. The numerical method proposed in the paper for solving the corresponding equations includes the use of smoothing splines. An important result is that the constructed identification algorithm has a low methodological error

Identification of Quadratic Volterra Polynomials in the “Input–Output” Models of Nonlinear Systems

In this paper, we propose a new algorithm for constructing an integral model of a nonlinear dynamic system of the “input–output” type in the form of a quadratic segment of the Volterra integro-power series (polynomial). We consider nonparametric identification of models using physically realizable piecewise linear test signals in the time domain. The advantage of the presented approach is to obtain explicit formulas for calculating the transient responses (Volterra kernels), which determine the unique solution of the Volterra integral equations of the first kind with two variable integration limits. The numerical method proposed in the paper for solving the corresponding equations includes the use of smoothing splines. An important result is that the constructed identification algorithm has a low methodological error