METHOD FOR AUTOMATIC COSTATE CALCULATION

A method for the automatic calculation of costates using only the resu lts obtained from direct optimization techniques is presented. The app roach exploits the relation between the time-varying costates and cert ain sensitivities of the variational cost function, a relation that al so exists between the Lagrangian multipliers obtained from a direct op timization approach and the sensitivities of the associated nonlinear- programming cost function. The complete theory for treating free, cont rol-constrained, interior-point-constrained, and state-constrained opt imal control problems is presented. As a numerical example, a state co nstrained version of the brachistochrone problem is solved and the res ults are compared to the optimal solution obtained from Pontryagin's m inimum principle. The agreement is found to be excellent.