A monotonic method for solving nonlinear optimal control problems with concave dependence on the state

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 performance when dealing with bilinear optimal control problems. This paper presents a unified formulation that can be applied to more nonlinear settings compatible with the hypothesis detailed below. 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 and compare it with the gradient algorithm.

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 with concave dependence on the state. International Journal of Control, 2011, 84 (3), pp.551--562. ⟨10.1080/00207179.2011.562548⟩. ⟨hal-00335297v4⟩