title: ÐÐµÐºÐ¾ÑÐ¾ÑÑÐµ Ð½ÐµÐºÐ¾ÑÑÐµÐºÑÐ½ÑÐµ Ð·Ð°Ð´Ð°ÑÐ¸ Ð² ÑÐµÐ¾ÑÐ¸Ð¸ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Some ill-posed problems in control theory
Creators: name: ÐÑÑÐµÐ¿Ð°Ð»Ð¾Ð²Ð°, ÐÐºÐ°ÑÐµÑÐ¸Ð½Ð°
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2022
Subjects: Ð¾Ð±ÑÐ°ÑÐ½Ð°Ñ Ð·Ð°Ð´Ð°ÑÐ°
Ð½ÐµÐºÐ¾ÑÑÐµÐºÑÐ½Ð¾ Ð¿Ð¾ÑÑÐ°Ð²Ð»ÐµÐ½Ð½Ð°Ñ Ð·Ð°Ð´Ð°ÑÐ°
inverse problem
ill-posed problem

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description: The subject of the graduate qualification work is: "Some ill-posed problems in control theory" This work is devoted to the theory of inverse problems, which is directly related to the problem of processing and interpreting experimental results. The purpose of this work is to consider the features of the formulation of inverse problems, the study and analysis of methods for solving the problem of determining the right side of a linear differential equation and the problems of interpreting the results of an experiment. The first chapter is an overview of the basic concepts of inverse and ill-posed problems. There are considered the problems of interpreting the results of an experiment, the concepts of correctly and ill-posed problems, and aspects of the formulation and solution of inverse problems are described. In the second section a number of methods for solving ill-posed problems, formulated in the form of operator equations of the first kind, are explored and analyzed. In the final chapter, an example of a theoretical inverse problem is presented using the general problem statement for determining the right side of a linear differential equation. To solve it, a method was proposed to reduce it to a linear Fredholm integral equation of the 1st kind with a kernel representing the Green's function.