Extended Runge-Kutta Method (ERKM) Algorithm for the Solution of Optimal Control Problems (OCP)

Mathew Folorunsho Akinmuyise; Kayode James Adebayo; Folorunsho Olabisi Adisa; Emmanuel Temitayo Olaosebikan; Sunday Oluwaseun Gbenro; Adejoke Olumide Dele-Rotimi; Abraham Adesoji Obayomi; Samuel Olukayode Ayinde

Autori

Mathew Folorunsho Akinmuyise Department of Mathematics, University of Education, Ondo, Ondo State, Nigeria
Kayode James Adebayo Department of Mathematics, Ekiti State University, Ado Ekiti, Ekiti State, Nigeria https://orcid.org/0000-0003-3684-6190
Folorunsho Olabisi Adisa Department of Mathematics, University of Education, Ondo, Ondo State, Nigeria
Emmanuel Temitayo Olaosebikan Department of Mathematics, Bamidele Olumilua University of Education, Science, and Technology, Ikere Ekiti, Ekiti State, Nigeria https://orcid.org/0000-0001-7625-9420
Sunday Oluwaseun Gbenro Department of Mathematics, Bamidele Olumilua University of Education, Science, and Technology, Ikere Ekiti, Ekiti State, Nigeria https://orcid.org/0000-0002-4013-8229
Adejoke Olumide Dele-Rotimi Department of Mathematics, Bamidele Olumilua University of Education, Science, and Technology, Ikere Ekiti, Ekiti State, Nigeria https://orcid.org/0000-0002-0120-8343
Abraham Adesoji Obayomi Department of Mathematics, Ekiti State University, Ado Ekiti, Ekiti State, Nigeria
Samuel Olukayode Ayinde Department of Mathematics, Ekiti State University, Ado Ekiti, Ekiti State, Nigeria

Cuvinte cheie:

Runge-Kutta Method , Extended Runge-Kutta Method , Optimal Control Problems , Hamiltonian , Control Variable

Rezumat

This paper discusses the adoption of the Runge-Kutta Method which is classically designed for solving First Order Differential equations to the solution of Optimal Control Problems (OCP) constrained by state differential equations. The Extended Runge-Kutta Method (ERKM) algorithm requires the formulation of the Hamiltonian from the given Optimal Control Problems. This will, in turn, be used to generate the appropriate multi-boundary conditions. The developed boundary conditions will then be embedded at each iteration of the ERKM algorithm to determine the values of the state, the co-state, and the control variables until a satisfactorily prescribed tolerance is reached. The ERKM algorithm was tested on some Lagrange forms of the Optimal Control Problems with successes recorded compared to existing results.