Using a Direct Multiple Shooting Method to an Optimal control problem Direct Multiple Shooting Method

Abstract

A multiple direct fire method is considered to solve optimal control problems. The multiple direct multiple shooting method is a numerical method for solving limit value problems. The method divides the interval over which a solution is sought into several smaller intervals, solves an initial value problem in each of the smaller intervals, and imposes additional matching conditions to form a solution over the entire interval. This method transforms an optimal control problem into a non-linear programming problem. To solve the latter problem, the zeros of the Lagrange Jacobian are computed using Newton’s method. Then, this method is illustrated by a numerical example and finally.