A monotonic method for solving nonlinear optimal control problems

Julien Salomon (1) , Gabriel Turinici (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

Initially introduced in the framework of quantum control, the so-called monotonic algorithms have demonstrated excellent numerical results when dealing with various bilinear optimal control problems. This paper presents a unified formulation that can be applied to more nonlinear settings. In this framework, we show that the well-posedness of the general algorithm is related to a nonlinear evolution equation. We prove the existence of the solution to this equation and give important properties of the optimal control functional. Finally we show how the algorithm works for selected models from the literature.

Mots clés: Monotonic algorithms; nonlinear control; optimal control; non-convex optimization

Domaines: Optimisation et contrôle [math.OC]

Julien Salomon, Gabriel Turinici. A monotonic method for solving nonlinear optimal control problems. 2010. ⟨hal-00335297v3⟩