Abstract
Nowadays, an Optimal Control problem tends to fall into the non-standard setting, especially in the economic field. This research deals with the non-standard Optimal Control problem with the involvement of the royalty payment. In maximizing the performance index, the difficulty arises when the final state value is unknown and resulting in the non-zero final costate value. In addition, the royalty function cannot be differentiated at a certain time frame. Therefore, an approximation of the hyperbolic tangent (tanh) was used as a continuous approach and the shooting method was implemented to settle the untangled issue. The shooting method was constructed in C ++ programming computer software. At the end of the study, the results produced are in the optimal solution. Future academics may build on this innovative discovery as they create mathematical modeling techniques to address practical economic issues. Moreover, the new method can advance the academic field in line with today’s technological advances.
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Acknowledgements
This research was supported by the Ministry of Higher Education (MOHE) through Fundamental Research Grant Scheme (FRGS/1/2021/STG06/UTHM/03/3). Thank you to Research Management Center (RMC), Universiti Tun Hussein Onn Malaysia (UTHM), for managing the research and publication process.
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Ahmad, W.N.A.W. et al. (2023). Solving the Royalty Payment Problem Through Shooting Method. In: Kaiser, M.S., Waheed, S., Bandyopadhyay, A., Mahmud, M., Ray, K. (eds) Proceedings of the Fourth International Conference on Trends in Computational and Cognitive Engineering. Lecture Notes in Networks and Systems, vol 618. Springer, Singapore. https://doi.org/10.1007/978-981-19-9483-8_20
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