New fundamental theory in solving the royalty payment problem / Wan Noor Afifah Wan Ahmad and Suliadi Firdaus Sufahani

This study aim to maximize the functional performance index of the non-classical Optimal Control problem. However, solving the problem, this project has to clarify a few constraints. Firstly, the final state is unknown which is resulting in the nonzero value of terminal costate. Besides, the royalty function is non-differentiable at certain process. Therefore, the indirect method was applied by involving new modified shooting method (Sufahani-Ahmad-Newton-Golden-Royalty Algorithm and Sufahani-Ahmad-Powell-Golden-Royalty Algorithm). The results comparison done with direct method (Euler, Runge-Kutta, Trapezoidal, Hermite-Simpson) as a validation process. Finally, it is expected that new modified shooting method yield highly accurate optimal solution compared to the direct method.