Automatic Solution of Optimal Control Problems II. First-Order Nonlinear Systems

An automatic method for obtaining the numerical solution for first-order nonlinear optimal control problems is described. The nonlinear two-point boundary value Euler-Lagrange equation is solved using the Newton-Raphson method for obtaining successive approximations of the solution. The derivatives required for the solution of the problem are computed automatically using the table method. The user of the program need only input the integrand of the cost functional and specify the initial conditions and the terminal time. None of the derivatives usually associated with the Euler-Lagrange equation and the Newton-Raphson method need be calculated by hand. An example is given with numerical results.