title: ÐÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ðµ Ð½ÐµÐ¹ÑÐ¾Ð½Ð½ÑÑ ÑÐµÑÐµÐ¹ Ð² Ð·Ð°Ð´Ð°ÑÐ°Ñ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½ÑÐ¼Ð¸ ÑÐ¸ÑÑÐµÐ¼Ð°Ð¼Ð¸
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: Application of neural networks in control problems of nonlinear systems
Creators: name: ÐÐµÐ¾Ð½ÑÑÐµÐ², Ð ÑÑÐ»Ð°Ð½
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: 2021
Subjects: ÐÐÐ-ÑÐµÐ³ÑÐ»ÑÑÐ¾Ñ
Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾-ÐºÐ²Ð°Ð´ÑÐ°ÑÐ¸ÑÐ½ÑÐ¹ ÑÐµÐ³ÑÐ»ÑÑÐ¾Ñ
Ð¿ÐµÑÐµÐ²ÐµÑÐ½ÑÑÑÐ¹ Ð¼Ð°ÑÑÐ½Ð¸Ðº
Ð¼Ð°ÑÑÐ½Ð¸Ðº Ð½Ð° ÑÐµÐ»ÐµÐ¶ÐºÐµ
Ð´Ð²Ð¾Ð¹Ð½Ð¾Ð¹ Ð¼Ð°ÑÑÐ½Ð¸Ðº Ð½Ð° ÑÐµÐ»ÐµÐ¶ÐºÐµ
Ð¾Ð±ÑÑÐµÐ½Ð¸Ðµ Ñ Ð¿Ð¾Ð´ÐºÑÐµÐ¿Ð»ÐµÐ½Ð¸ÐµÐ¼
Ð½ÐµÐ¹ÑÐ¾Ð½Ð½ÑÐµ ÑÐµÑÐ¸
PID-regulator
linear-quadratic regulator
inverted pendulum
inverted pendulum on a cart
double invetrted pendulum on a cart
reinforcement learning
neural networks

description: Ð Ð°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð¿ÑÐ¸Ð¼ÐµÐ½Ð¸Ð¼Ð¾ÑÑÐ¸ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ ÑÐ¸ÑÑÐµÐ¼Ð°Ð¼Ð¸ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¾Ð±ÑÑÐµÐ½Ð¸Ñ Ñ Ð¿Ð¾Ð´ÐºÑÐµÐ¿Ð»ÐµÐ½Ð¸ÐµÐ¼ Ð¸ Ð½ÐµÐ¹ÑÐ¾Ð½Ð½ÑÑ ÑÐµÑÐµÐ¹, Ð° ÑÐ°ÐºÐ¶Ðµ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ð¸Ñ Ñ ÐºÐ»Ð°ÑÑÐ¸ÑÐµÑÐºÐ¸Ð¼Ð¸ Ð¼ÐµÑÐ¾Ð´Ð°Ð¼Ð¸ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ, ÑÐ°ÐºÐ¸Ð¼Ð¸ ÐºÐ°Ðº ÐÐÐ-ÑÐµÐ³ÑÐ»ÑÑÐ¾Ñ Ð¸ Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾-ÐºÐ²Ð°Ð´ÑÐ°ÑÐ¸ÑÐ½ÑÐ¹ ÑÐµÐ³ÑÐ»ÑÑÐ¾Ñ. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¿ÑÐ¾Ð²Ð¾Ð´Ð¸ÑÑÑ Ð½Ð° Ð¿ÑÐ¸Ð¼ÐµÑÐµ Ð·Ð°Ð´Ð°ÑÐ¸ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ Ð¼Ð°ÑÑÐ½Ð¸ÐºÐ¾Ð¼, Ð´Ð²Ð¾Ð¹Ð½ÑÐ¼ Ð¼Ð°ÑÑÐ½Ð¸ÐºÐ¾Ð¼ Ð½Ð° ÑÐµÐ»ÐµÐ¶ÐºÐµ Ð¸ Ð¿ÐµÑÐµÐ²ÐµÑÐ½ÑÑÑÐ¼ Ð¼Ð°ÑÑÐ½Ð¸ÐºÐ¾Ð¼ Ð½Ð° ÑÐµÐ»ÐµÐ¶ÐºÐµ. ÐÐºÑÑÐ°Ð»ÑÐ½Ð¾ÑÑÑ ÑÐ°Ð±Ð¾ÑÑ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÑÐµÑÑÑ ÑÐµÐ¼, ÑÑÐ¾ ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²Ð¾ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½ÑÐ¼Ð¸ ÑÐ¸ÑÑÐµÐ¼Ð°Ð¼Ð¸ Ð¾ÑÐ½Ð¾ÑÐ¸ÑÐµÐ»ÑÐ½Ð¾ Ð½ÐµÐ²ÐµÐ»Ð¸ÐºÐ¾, Ð¿ÑÐ¸ÑÐµÐ¼ ÑÐ°ÑÑÑ Ð¸Ð· ÑÑÐ¸Ñ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð¿Ð¾Ð´ÑÐ°Ð·ÑÐ¼ÐµÐ²Ð°ÐµÑ Ð»Ð¸Ð½ÐµÐ°ÑÐ¸Ð·Ð°ÑÐ¸Ñ Ð¾ÐºÐ¾Ð»Ð¾ Ð½ÐµÐºÐ¾ÑÐ¾ÑÐ¾Ð¹ ÑÐ¾ÑÐºÐ¸ ÑÐ°Ð·Ð¾Ð²Ð¾Ð³Ð¾ Ð¿ÑÐ¾ÑÑÑÐ°Ð½ÑÑÐ²Ð° ÑÐ¸ÑÑÐµÐ¼Ñ. ÐÐ¾ÑÑÐ¾Ð¼Ñ Ð¼ÐµÑÐ¾Ð´Ñ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ, Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð½ÑÐµ Ð½Ð° Ð¾Ð±ÑÑÐµÐ½Ð¸Ð¸ Ñ Ð¿Ð¾Ð´ÐºÑÐµÐ¿Ð»ÐµÐ½Ð¸ÐµÐ¼, Ð¼Ð¾Ð³ÑÑ ÑÐ°ÑÑÐ¸ÑÐ¸ÑÑ ÑÐ¿ÐµÐºÑÑ ÑÐµÑÐ°ÐµÐ¼ÑÑ Ð·Ð°Ð´Ð°Ñ, Ð½Ðµ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÑ Ð¿ÑÐ¸ ÑÑÐ¾Ð¼ Ð»Ð¸Ð½ÐµÐ°ÑÐ¸Ð·Ð°ÑÐ¸Ð¸ Ð¸Ð»Ð¸ Ð²Ð¾Ð¾Ð±ÑÐµ Ð½Ðµ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÑ Ð¿Ð¾ÑÑÐ¸ Ð½Ð¸ÐºÐ°ÐºÐ¸Ñ Ð´Ð°Ð½Ð½ÑÑ Ð¾ ÑÐ¸ÑÑÐµÐ¼Ðµ. Ð¢Ð°ÐºÐ¶Ðµ ÑÐ°Ð±Ð¾ÑÐ° ÑÐ²Ð»ÑÐµÑÑÑ Ð°ÐºÑÑÐ°Ð»ÑÐ½Ð¾Ð¹ Ð¸ Ð² ÑÐ¸Ð»Ñ Ð½ÐµÐ±Ð¾Ð»ÑÑÐ¾Ð³Ð¾ ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²Ð° ÑÐ°Ð±Ð¾Ñ Ð½Ð° ÑÑÑ ÑÐµÐ¼Ñ Ð½Ð° ÑÑÑÑÐºÐ¾Ð¼ ÑÐ·ÑÐºÐµ, Ð¿Ð¾ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ñ ÑÐ°Ð±Ð¾ÑÐ°Ð¼Ð¸ Ð½Ð° Ð°Ð½Ð³Ð»Ð¸Ð¹ÑÐºÐ¾Ð¼.
description: The work is devoted to the study of the applicability of systems control methods using reinforcement learning and neural networks, as well as their comparison with classical control methods such as a PID controller and a linear- quadratic controller. The study is carried out on the example of the problem of controlling a pendulum, a double pendulum on a trolley and an inverted pendulum on a trolley. The relevance of the work is determined by the fact that the number of control methods for nonlinear systems is relatively small, and some of these methods imply linearization around a point in the phase space of the system. Therefore, reinforcement learning-based control methods can expand the range of problems to be solved without using linearization or using almost no data about the system at all. Also, the work is relevant and due to the small number of works on this topic in Russian, compared to works in English.