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Taylor and Francis Group, International Journal of Control, 3(84), p. 551-562

DOI: 10.1080/00207179.2011.562548

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

Journal article published in 2011 by Julien Salomon, Gabriel Turinici ORCID
This paper is available in a repository.
This paper is available in a repository.

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Abstract

Initially introduced in the framework of quantum control, the so-called monotonic algorithms have demonstrated very good numerical performance when dealing with bilinear optimal control problems. This article presents a unified formulation that can be applied to more general 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 the evolution equation and give important properties of the optimal control functional. Finally we show how the algorithm works for selected models from the literature. We also compare the algorithm with the gradient algorithm.