Automatic solution of optimal control problems III: Differential and integral constraints

An automatic method for obtaining the numerical solution of a certain class of second-order nonlinear optimal control problems with differential and integral constraints is described. The nonlinear two-point boundary value problem 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 the differential constraints and specify the intial conditions and the terminal time. None of the derivatives usually associated with Pontryagin´s maximum principle and the Newton-Raphson method need be calculated by hand. A set of FORTRAN subroutines in the program for solving the optimal control problems is described. An example is given with numerical results.