ABSTRACT
This chapter presents several singular optimal control problems that have puzzled researchers for over two decades, three of which were solved by Luus. It shows that even simple-looking problems can be very challenging, and provides guidelines of how to approach a problem when the solution does not arise in a single computer run. The chapter provides a realistic optimal control problem from chemical engineering that has been very difficult to solve by using methods based on Pontryagin’s maximum principle, but can be solved quite readily with iterative dynamic programming. It uses stages of varying length, and a quadratic penalty function with a shifting term to solve singular optimal control problems. For integration, the chapter uses the subroutine DVERK with a local error tolerance. One of the earliest examples tried with iterative dynamic programming is the singular control problem used by Yeo to illustrate the use of quasilinearization to solve nonlinear singular control problems.
