Generalized Regularization of Constrained Optimal Control Problems
- 1 July 2022
- journal article
- research article
- Published by American Institute of Aeronautics and Astronautics (AIAA) in Journal of Spacecraft and Rockets
- Vol. 59 (4), 1096-1110
- https://doi.org/10.2514/1.a35229
Abstract
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.Keywords
Funding Information
- Laboratory Directed Research and Development (DE-NA0003525)
This publication has 38 references indexed in Scilit:
- Handling constraints in optimal control with saturation functions and system extensionSystems & Control Letters, 2010
- Direct Trajectory Optimization and Costate Estimation via an Orthogonal Collocation MethodJournal of Guidance, Control, and Dynamics, 2006
- An Optimal Control Model of Forest Carbon SequestrationAmerican Journal of Agricultural Economics, 2003
- New smoothing techniques for solving bang–bang optimal control problems—numerical results and statistical interpretationOptimal Control Applications and Methods, 2002
- Entry Trajectory Tracking Law via Feedback LinearizationJournal of Guidance, Control, and Dynamics, 1998
- Stabilized continuation method for solving optimal control problemsJournal of Guidance, Control, and Dynamics, 1994
- Numerical solution of differential-algebraic equations in mechanical systems simulationPhysica D: Nonlinear Phenomena, 1992
- The Numerical Solution of Higher Iindex Differential/Algebraic Equations by Implicit MethodsSIAM Journal on Numerical Analysis, 1989
- Computation of optimal singular controlsIEEE Transactions on Automatic Control, 1970
- Singular solutions in problems of optimal controlIEEE Transactions on Automatic Control, 1963