Connection between singular arcs in optimal control using bridges. Physical occurence and Mathematical model

Toufik Bakir (1) , Bernard Bonnard (2, 3) , Jérémy Rouot (2, 4)

1 UB - Université de Bourgogne
2 IMB - Institut de Mathématiques de Bourgogne [Dijon]
3 McTAO - Mathematics for Control, Transport and Applications
4 EPF [Troyes]

In the time minimal control problem, singular arcs are omnipresent to determine the optimal solutions and leads to the well known turnpike phenomenon [1]. Very recently, this connection between singular arcs using a bang arc was shown to be relevant to saturate a single spin in Magnetic Resonance Imaging. Based on this example we propose a mathematical model to analyze such connection, which is called a bridge. This is applied to compute bridges in the optimization of chemical reaction networks using temperature control.

Mots clés: Pontryagin maximum principle; Singularity theory; Geometric control

Domaines: Optimisation et contrôle [math.OC]

Toufik Bakir, Bernard Bonnard, Jérémy Rouot. Connection between singular arcs in optimal control using bridges. Physical occurence and Mathematical model. CDC 2019 - 58th Conference on Decision and Control, Dec 2019, Nice, France. ⟨10.1109/CDC40024.2019.9029880⟩. ⟨hal-02050014v3⟩