Differential continuation for regular optimal control problems

Jean-Baptiste Caillau (1) , Olivier Cots (1) , Joseph Gergaud (2, 3)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 IRIT-APO - Algorithmes Parallèles et Optimisation
3 Toulouse INP - Institut National Polytechnique (Toulouse)

Regular control problems in the sense of the Legendre condition are defined, and second-order necessary and sufficient optimality conditions in this class are reviewed. Adding a scalar homotopy parameter, differential pathfollowing is introduced. The previous sufficient conditions ensure the definiteness and regularity of the path. The role of AD for the implementation of this approach is discussed, and two examples excerpted from quantum and space mechanics are detailed.

Mots clés: Optimal control; Second-order conditions; Conjugate points; Differential homotopy; Automatic differentiation

Domaines: Optimisation et contrôle [math.OC]

Jean-Baptiste Caillau, Olivier Cots, Joseph Gergaud. Differential continuation for regular optimal control problems. Optimization Methods and Software, 2012, 27 (2), pp.177-196. ⟨10.1080/10556788.2011.593625⟩. ⟨hal-00641908⟩