Article 6220

Title of the article

TO THE PRACTICAL IMPLEMENTATION OF SOLVING THE OPTIMAL CONTROL PROBLEM 

Authors

Diveev Askhat Ibragimovich, doctor of technical sciences, professor, chief researcher, head of the department of robotics control, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences (42/2 Vavilova street, Moscow, Russia), E-mail: aidiveev@mail.ru
Shmalko Elizaveta Yurievna, candidate of technical sciences, senior researcher, department of robotics control, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences (42/2 Vavilova street, Moscow, Russia), E-mail: e.shmalko@gmail.com 

Index UDK

51-74, 519.6 

DOI

10.21685/2307-4205-2020-2-6 

Abstract

Background. Ubiquitous robotics and modern high-performance robot manufacturing technology require developers of automatic control systems to use high-performance methods for creating control systems for these robots. The usual procedure for constructing control systems includes developing a mathematical model of a control object, a robot, formalizing a control problem, applying one of the existing methods or developing a new one to solve a formal mathematical problem and implementing the resulting solution on an on-board processor of a control object, a robot. One of the most well-known control problems is the optimal control problem formulated by L.S. Pontryagin. The book itself repeatedly indicates the technical orientation of the results obtained, in particular, in the annotation to the monograph it is said “This principle (meaning the Pontryagin’s maximum principle) will allow solving a number of mathematical and applied problems ...”, then in the same place “The book is … a manual that can be used by an engineer and designer. ”. As further studies have shown, even the numerical solution of the boundary value problem, which the Pontryagin’s maxim principle leads to, is a rather difficult problem. But, if this problem is somehow solved today using modern computers, the question of what to do next with the resulting solution and how to implement it in a real control object remains open. It is believed that to implement the solution, it is necessary to build an additional stabilization system, but there is no consensus on how to do this. The present work is devoted to the study of meth ods for implementing the solution of the optimal control problem. In connection with the tightening of the time requirements for the creation of control systems for robotic devices, this task becomes extremely urgent.
Materials and methods. The paper presents studies of various methods for the control system synthesis for stabilizing the movement of a control object along a given path. Both classical technical and analytical approaches, as well as modern computational methods based on the use of evolutionary algorithms are considered. As one of the alternatives, it is proposed to reformulate the optimal control problem with the inclusion of the stabilization system synthesis problem in its formulation.
Results. Various approaches to the implementation of the solution of the optimal control problem in the control system of a real object are presented. Advantages and disadvantages of the considered methods for stabilization systems synthesis for the motion of a control object along a given path are demonstrated. The optimal control problem is formulated, which includes the stage of synthesis of a stabilization system for movement along an optimal trajectory.
Conclusions. From the point of view of applied implementation, various methods of the system synthesis for stabilizing a control object along a given path to achieve the goal are considered and investigated. The results of the study show that either the stabilization systems developed by well-known methods do not provide the exact movement of the control object along a given trajectory while maintaining the value of the quality criterion, or the formulation of the control synthesis problem is much more complicated than the optimal control problem and its solution requires the development of new computational methods. All stabilization systems change the mathematical model of the control object, which was considered when solving the optimal control problem, therefore, from the point of view of the initial quality criterion, movement along a given trajectory of a real object is not optimal.

Key words

unmanned vehicle, predictive control model, neural network, particle swarm optimization method 

Download PDF

 

Дата создания: 17.07.2020 11:13
Дата обновления: 17.07.2020 12:49