Publications

Investigation of control regularization functions in bang-bang/singular optimal control problems

Heidrich, Casey R.; Sparapany, Michael J.; Grant, Michael J.

Problems in optimal control may exhibit a bang-bang or singular control structure. These qualities pose challenges with indirect solution methods when the control law is discontinuous or indefinite. Recent efforts in control regularization strategies have sought to overcome these difficulties. These methods approximate a smoothed mapping of the constrained multi-stage Hamiltonian boundary value problem, resolving the singular/bang arcs into a single-stage problem. This work investigates the use of control saturation functions for error-control regularization. A key feature of the new approach is to eliminate ambiguity of the control law derived from the necessary conditions for optimality. The method is shown to have improved stability in numerical continuation due to the removal of small error terms from the control law. A well-known classical problem with analytical solutions is studied, as well as a more applied problem involving atmospheric flight of a maneuvering reentry vehicle.