Strong and weak solutions of fuzzy nonlinear optimal control problems via a Jacobi-based neural network scheme

Articles in Press

Document Type : Research Paper

Authors

Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran.

Abstract

In this paper, an artificial neural network architecture is proposed for solving a class of fuzzy optimal control problems.
At the first step, we consider the Pontryagin minimum principle for the mentioned problems.
The necessary optimality conditions for these problems are stated in the form of two-point boundary value problems.
Then, for the first time, a neural network solution method is introduced in which Jacobi functions are employed as activation functions in one of the hidden layers to approximate solutions to two-point boundary value problems. This neural network uses roots of Jacobi polynomials as the training dataset, and the Levenberg-Marquardt algorithm is chosen as the optimizer.
By relying on the ability of the generalized fuzzy hyperbolic models as function approximator,
the trial solutions of variables are substituted in the related two-point boundary value problem. The
obtained
algebraic nonlinear equations system is then reduced into an error function minimization problem.
A learning
scheme based on
the Levenberg-Marquardt algorithm is employed as the optimizer
to derive the adjustable parameters of fuzzy solutions.
To show the effectiveness of the presented neural network, some numerical results are provided.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 10 May 2026

Files

History

  • Receive Date: 09 April 2025
  • Revise Date: 27 February 2026
  • Accept Date: 09 May 2026

Share

How to cite

Statistics