FINITE-DIFFERENCE SCHEME FOR AUTOMATIC COSTATE CALCULATION

A method for the automatic calculation of costates using only results obtained from direct optimization techniques is presented. The approac h is based on finite differences and exploits the relation between the costates and certain sensitivities of the cost function. The complete theory for treating free, control constrained, interior-point constra ined, and state constrained optimal control problems is presented. An important advantage of the method presented here is that it does not r equire a priori identification of the optimal switching structure. As a numerical example, a state constrained version of the Brachistochron e problem is solved, and the results are compared to the optimal solut ion obtained from Pontryagin's minimum principle. The agreement is fou nd to be excellent.