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