Time Minimal Syntheses in the Abnormal Case using Geometric and Computational Techniques

Olga Assainova (1) , Jérémy Rouot (2)

1 LABISEN-LSL - Light Scatter Learning
2 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

This article deals with the optimization of chemical network in the frame of geometric optimal control and singularity theory. The objective is to classify the generic syntheses for analytic systems of the form q̇(t) = X(q(t))+u(t) Y (q(t)), where the aim is to reach in minimum time a terminal manifold of codimension one. We restrict the study to the three dimensional case considering the McKeithan network for which situations up to codimension 3 have to investigated. We develop symbolic algorithms to derive semi-normal forms and to compute approximations of the strata of the singular set to obtain classification in the generic cases and to illustrate the role of singularity theory in geometric control, in relation with abnormal geodesics and regularity of the value function.

Mots clés: Regularity of the value function; Time minimal syntheses; Geometric optimal control; Chemical reaction networks

Domaines: Optimisation et contrôle [math.OC]

Olga Assainova, Jérémy Rouot. Time Minimal Syntheses in the Abnormal Case using Geometric and Computational Techniques. 18th IFAC Workshop on Control Applications of Optimization CAO 2022, Jul 2022, Gif sur Yvette, France. ⟨10.1016/j.ifacol.2022.08.080⟩. ⟨hal-03551676v2⟩