Comparative Analysis of the Convergence of the Population-Based Algorithm and the Gradient Algorithm for Optimizing the Neural Network Solution of the Optimal Control Problems

DOI

10.2991/csit-19.2019.20How to use a DOI?

Keywords

nonlinear optimization problem, neural network, gradient descent method, gravity search algorithm, population algorithm

Abstract

In this paper, we consider the functional representation of the solution of the optimal control problem without restrictions using the neural network approach, which allows us to find a functional representation of the solution. Based on the necessary first-order optimality conditions, the original problem is reduced to a nonlinear optimization problem where the weights and displacements associated with all neurons are unknown. The minimization of the error function of the neural network solution is carried out by the gradient descent method, as well as by the population gravity search algorithm. Several examples demonstrating the effectiveness of the considered methods are considered. A comparative analysis of the convergence of the algorithms used is carried out. The study showed that the gravitational search algorithm, which requires the least number of iterations to achieve accuracy, is more efficient. Such an effect may be due to the gully of the minimized Lagrange function, as well as with other factors that require additional research.

Copyright

© 2019, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Irina Bolodurina
AU  - Lubov Zabrodina
PY  - 2019/12
DA  - 2019/12
TI  - Comparative Analysis of the Convergence of the Population-Based Algorithm and the Gradient Algorithm for Optimizing the Neural Network Solution of the Optimal Control Problems
BT  - Proceedings of the 21st International Workshop on Computer Science and Information Technologies (CSIT 2019)
PB  - Atlantis Press
SP  - 119
EP  - 124
SN  - 2589-4900
UR  - https://doi.org/10.2991/csit-19.2019.20
DO  - 10.2991/csit-19.2019.20
ID  - Bolodurina2019/12
ER  -