A nonstandard optimal control problem arising in an economics application: for royalty payment with piecewise function

• Main Author: Wan Ahmad, Wan Noor Afifah
• Format: Thesis
• Language: English; English; English
• Published: 2018
• Subjects: QA273-280 Probabilities. Mathematical statistics
• Online Access: http://eprints.uthm.edu.my/331/1/24p%20WAN%20NOOR%20AFIFAH%20WAN%20AHMAD.pdf; http://eprints.uthm.edu.my/331/2/WAN%20NOOR%20AFIFAH%20WAN%20AHMAD%20COPYRIGHT%20DECLARATION.pdf; http://eprints.uthm.edu.my/331/3/WAN%20NOOR%20AFIFAH%20WAN%20AHMAD%20WATERMARK.pdf; http://eprints.uthm.edu.my/331/

A current Optimal Control (OC) problem in the region of financial aspects has numerical properties that do not fall into the standard OC problem formulation. In this study, the state value at the final time is y T   z where it is free and a priori unknown. Furthermore, the Lagrangian integrand in the functional is a piecewise constant system of the unknown value y T . This is not categorized, as in a standard OC problem, and cannot be settled by utilizing Pontryagin's Minimum Principle with the standard boundary conditions at the final time. In the standard case, a free final state value y T  yields a necessary boundary condition pT   0 where pt  is the costate variable. Since the integrand is an element of y T , the new necessary condition is that y T  ought to be equivalent to a certain integral that is a continuous system of y T   z. This study presents a continuous approximation of the piecewise constant integrand function by utilizing a hyperbolic tangent (tanh) approach, and solves a case utilizing a C++ shooting algorithm with a Newton iteration to take care of the Two-Point Boundary Value Problem (TPBVP). The minimizing free value y T  is computed in an outer loop iteration utilizing the Golden Section Search algorithm. At the end of the study, a comparative discrete-time nonlinear programming (NLP) results are also presented.