Publications

Journal of Spacecraft and Rockets

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

Constraints in optimal control problems introduce challenges with traditional indirect methods. Bang-bang/ singular solutions with discontinuous or indefinite control laws add further difficulty in numerical solution. Recent efforts in control regularization strategies have sought to overcome these limitations. Regularization generates a smoothed constraint transformation of a multiphase Hamiltonian boundary value problem to a single-phase unconstrained problem. This work develops a new approach to regularization using orthogonal error-control saturation functions. The method is developed for problems in bang-bang/singular form. The method is then applied to problems of general Hamiltonian structure using system extension and differential control. Applications in state constraint regularization are discussed. A key feature of the new approach is to eliminate ambiguity of the control law derived from the first-order necessary conditions of optimality. Results show desirable stability and convergence in numerical continuation. The method is applied to classical problems in optimal control, as well as problems of interest in aerospace mission design.

AIAA Scitech 2021 Forum

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.

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

Abstract not provided.