Some directs numerical methods for solving the nonlinear optimal control problem practical in aeronautic

Abstract

In this study, we have implemented direct numerical methods to convert the continuous optimal control problem into a nonlinear optimization problem. We used three discretization techniques: the Euler method, the second-order Runge-Kutta method, and the fourth-order Runge-Kutta method. Subsequently, the resulting non-linear optimization problem was solved using MATLAB's fmincon function. To evaluate the efficiency and accuracy of the proposed approach, we modeled a nonlinear optimal control problem relevant to aeronautics. Our objective was to minimize the travel time of a rocket from an initial point to a final point at a specified altitude, considering aerodynamic forces and gravity, with the control variable being the rocket's heel angle. To compare the different methods, we developed a MATLAB implementation and showcased various simulation results.