A Study of Approximated Solutions of the Optimal-Control Problems Governed by Initial Value Problems using Basic Functions

Abstract

The problem of determining a control law for a given system is addressed by optimal control(OC). Using fundamental functions, a computational method for addressing optimum control problems (OCPs). This technique relies on the use of fundamental functions to approximate the problem's solution. In fact, some of the coefficients in the optimal formula are determined by initial or boundary conditions(BCs), while others are approximated using the minimizing calculation. On the other hand, an OCP transforms into a numerically solvable optimization problem. The approximate value of the performance index is calculated using this numerical method. Approximate results for several test conditions are provided to demonstrate the method's efficiency and applicability