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

Abstract

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.