Solving Royalty Problem Through a New Modified Shooting Method
Wan Noor Afifah Wan Ahmad1, Suliadi Firdaus Sufahani2, Alan Zinober3
1Wan Noor Afifah Wan Ahmad, Department of Mathematics and Statistic, Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn Malaysia, Pagoh Educational Hub, 84600 Pagoh, Muar, Johor.
2Suliadi Firdaus Sufahani, Department of Mathematics and Statistic, Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn Malaysia, Pagoh Educational Hub, 84600 Pagoh, Muar, Johor.
3Alan Zinober, School of Mathematics and Statistics, University of Sheffield, Sheffield S3 7RH, United Kingdom.
Manuscript received on 15 April 2019 | Revised Manuscript received on 20 May 2019 | Manuscript published on 30 May 2019 | PP: 469-475 | Volume-8 Issue-1, May 2019 | Retrieval Number: A3498058119/19©BEIESP
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: Optimal Control (OC) study in the recent year has been an interest of many young researchers, especially in the nonstandard OC context. The same goes for this research’s intention. The nonstandard problem dealing with the free final state value y (T) where the integrand of the performance index relies on the y (T) value. In addition, the final costate value p (T) is said to be a nonzero solution. Contrastly, in the standard setting, the boundary condition p (T) = 0 and the integrand are independent to the known final state value y (T). This paper is interested in solving the nonstandard OC problem through modified shooting method with the involvement of 4-stages piecewise constant integrand system for the royalty function, ρ . This system is then being converted into a continuous approximation of hyperbolic tangent (tanh) function in order to allow the system to become differentiable at any process. The outcome of the modified shooting method will be obtained by running the program in C++ programming language and will be compared with the discretised values as a validation procedure.
Index Terms: Discretisation, Hyperbolic Tangent Function, Optimal Control, Royalty Problem, Shooting Method.
Scope of the Article: Problem Solving and Planning