Optimal Control Problem With Non-Standard Conditions: Direct and Indirect Approaches

Abstract

In relation to the non-standard Optimal Control problem, this paper focuses on maximizing the performance index. The model equation involved the royalty payment function that cannot be differentiated at a certain level. In addition, the state and costate at the final time are said to be unspecified and not equal to zero, respectively. This difficulty was avoided by using a continuous approach. The discrete royalty function is converted in this instance using the hyperbolic tangent function. After that, the issue was resolved indirectly by integrating the shooting method with the Newton and Golden Section Search methods. The program is constructed by using the C++ programming language. The shooting result was then compared with the indirect method, which involved the Runge–Kutta method. Both methods are expected to yield an accurate solution that is optimal (maximize) performance index. This brilliant idea can be implemented in real-world problems, especially in the academic field, so that the method used is up to date along with the current need.