Improve Numerical Method for Solving Optimal Control Problems Using Predictor-Corrector Method

Authors

  • Y. Ajiya Department of Mathematics, Faculty of Science, Gombe State University, Gombe, Nigeria
  • A. Ishaku Department of Mathematics, Faculty of Science, Gombe State University, Gombe, Nigeria
  • A. U Kinafa Department of Mathematics, Faculty of Science, Gombe State University, Gombe, Nigeria
  • S. B Muhammad Department of Statistics, Federal University of Agriculture Makurdi, Benue, Nigeria.
  • B. P Chajire Department of Mathematics, Faculty of Science, Gombe State University, Gombe, Nigeria

DOI:

https://doi.org/10.56892/bima.v7i02.%201.457

Keywords:

Control variable, forward-backward sweep algorithm, predictor-corrector method, Runge-Kutta method, state variable.

Abstract

In this paper, the numerical solution of optimal control problems using predictor-corrector methods with a forward-backward sweep algorithm is presented. The algorithm is developed to solve the state variable forward in time and the adjoint system alongside the control functions backward in time. The starting values of the methods were obtained using the classical Runge-Kutta method. The proposed algorithm is implemented using MAPLE 18 software to avoid a computational error. Some numerical examples are presented to illustrate the accuracy, reliability, consistency, and effectiveness of the present method. Finally, the results obtained were compared with the exact solution, and it performed favorably.

 

 

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Published

2023-08-09

How to Cite

Y. Ajiya, A. Ishaku, A. U Kinafa, S. B Muhammad, & B. P Chajire. (2023). Improve Numerical Method for Solving Optimal Control Problems Using Predictor-Corrector Method. BIMA JOURNAL OF SCIENCE AND TECHNOLOGY (2536-6041), 7(02. 1), 65-75. https://doi.org/10.56892/bima.v7i02. 1.457

Issue

Vol. 7 No. 02. 1 (2023): SPECIAL ISSUE

Section

Articles