A two-step method for solving singular control problems

A two-step method for solving singular control problems is presented. Iterative dynamic programming (IDP), an algorithm based on dynamic programming, is used as the optimisation procedure. A preliminary IDP run with fixed time stages is used to locate the position of the singular arcs. The result is then refined by incorporating a continuous equation for the singular section, in an IDP run with flexible stage lengths. The use of a continuous equation for the singular arc results in better values of the performance index than previously obtained, using IDP. A significant reduction in computation time is observed for problems with a single control variable. The information from the preliminary run was found to be useful in solving problems where state constraints are additionally present. Although IDP is used as the optimisation method in this paper, the idea is general in nature and can be applied to any heuristics based optimisation procedure.