Solving royalty problem through a new modified shooting method

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 relies on the y(T) where the integrand of the performance index 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, p. 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.