Section: New Results

Averaging in control

Participants : Bernard Bonnard, Helen-Clare Henninger, Jean-Baptiste Pomet.

A paper on the construction and properties of an “average control system” [1] appeared this year, it is based on Alex Bombrun's doctoral work (2007). It connects solutions of highly oscillating control systems to those of an average control system, when the frequency of oscillation goes high. It also gives a better ground to averaging for minimum time.

This average system in the case of minimum time for low thrust orbit transfer in the two body problem is currently being explored, in particular the study of its inherent singularities. In [16] we give some properties of this system, like geodesic convexity, and compare it with the one obtained for minimum energy, and Helen Henninger's PhD aims at going further in this direction and then apply this local study to real missions, possibly in a three-body environment.