Abstract

Numerical Solution of Optimal Control Problems Using Improved Euler Method

M. F. Akinmuyise1 ; S. O. Olagunju2 ; S. A. Olorunsola3

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This paper discussed the extension of the improved Euler method to the solution of optimal control problems with the state constrained by differential equations. The method combined the classical method with the numerical algorithm of Euler by embedding each of the boundary conditions from the Hamiltonian into the algorithm of Euler and allow the system to undergo the iterative process of the Euler until the gradient norm of the objective function approaches certain tolerance(according to [1], [2], [12] and [13]. A suitable formula for updating the control variable u t() as akin to [2] at each one-dimensional search was developed. The numerical results generated by this process demonstrated the stability and robustness of the method as it triumphs over reasonable number of problems. Keywords: Euler method, Optimal control problems, Hamiltonian, Algorithm process, Control variable.

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