Application of the finite element method to an optimal control problem

The finite element method is applied to a typical problem in the optimal control theory. A finite element formulation is first set up, and then applied, as an example, to a problem of minimizing the transfer time of a low-thrust rocket vehicle between the orbits of earth and Mars. A procedure which combines the gradient projection technique with the Newton-Raphson method is introduced to obtain numerically the solution of the minimum time transfer problem from the discretized functional. Numerical results show that the application of the finite element method to optimal control problems seems promising as well as encouraging.