Open AccessModified Gradient Flow Method for Solving One-Dimensional Optimal Control Problem Governed by Linear Equality Constraint
Author(s) -
O. Olotu,
Charles A. Aladesaye,
Kazeem Adebowale Dawodu
Publication year - 2022
Publication title -
journal of the nigerian society of physical sciences
Language(s) - English
Resource type - Journals
ISSN - 2714-4704
DOI - 10.46481/jnsps.2022.589
Subject(s) - discretization , mathematics , balanced flow , gradient method , convergence (economics) , constraint (computer aided design) , mathematical optimization , flow (mathematics) , quadratic equation , optimal control , mathematical analysis , geometry , economics , economic growth
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