A Finite Difference Based Scheme for Automatic Costate Calculation

摘要

A method for the automatic calculation of costates using only results obtained from direct optimization techniques is presented. The approach is based on finite differences and exploits the relation between the costates and certain sensitivities of the cost function. The complete theory for handling free, control constrained, and state constrained optimal control problems is presented in this paper. An important advantage of the method presented here is that it does not require a priori identification of the optimal switching structure. As a numerical example, a state constrained version of the Brachistochrone problem is solved and the results are compared to the optimal solution obtained from Pontryagin's Minimum Principle. The agreement is found to be excellent.