Modified Gradient Flow Method for Solving One-Dimensional Optimal Control Problem Governed by Linear Equality Constraint

Olusegun Olotu; Charles  Aladesaye; Kazeem Adebowale Dawodu

doi:10.46481/jnsps.2022.589

Authors

Olusegun Olotu Department of Mathematical Sciences,The Federal University of Technology Akure, Nigeria
Charles Aladesaye Dept. of Mathematics, School of Science, College of Education, Ikere-Ekiti, Ekiti State, Nigeria
Kazeem Adebowale Dawodu
kadawodu@futa.edu.ng
Department of Mathematical Sciences,The Federal University of Technology Akure, Nigeria

Keywords:

Optimal Control, Gradient Flow, three-level splitting parameters, discretization scheme, linear and quadratic convergence

Abstract

This study presents a computational technique developed for solving linearly constraint optimal control problems using the Gradient Flow Method. This proposed method, called the Modified Gradient Flow Method (MGFM), is based on the continuous gradient flow reformulation of constrained optimization problem with three-level implicit time discretization scheme. The three-level splitting parameters for the discretization of the gradient flow equations are such that the sum of the parameters equal to one (\theta₁ + \theta₂ +\theta₃=1). The Linear and quadratic convergence of the scheme were analyzed and were shown to have first order scheme when each parameter exist in the domain [0, 1] and second order when the third parameter equal to one. Numerical experiments were carried out and the results showed that the approach is very effective for handling this class of constrained optimal control problems. It also compared favorably with the analytical solutions and performed better than the existing schemes in terms of convergence and accuracy

Dimensions

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