Time Minimal Syntheses in the Exceptional 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 dq/dt = X(q)+u Y (q), where the aim is to reach in minimum time a terminal manifold of codimension one. We develop symbolic algorithms to compute approximations of the strata of the singular set to derive the topological 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, solution of Hamilton-Jacobi-Bellman equation.

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

Domaines: Optimisation et contrôle [math.OC]

Olga Assainova, Jérémy Rouot. Time Minimal Syntheses in the Exceptional Case using Geometric and Computational Techniques. 2022. ⟨hal-03551676v1⟩