Bombrun, Alex (2007) Low thurst orbital transfer: optimality and feedback. PhD thesis Informatique temps réel, robotique, automatique, CMA - Centre de Mathématiques Appliquées, ENSMP p.113.

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Abstract

This thesis presents a study of the low thrust two body control system and in particular orbital transfer problems. After a controllability study, we focus on the link between the optimal control in minimum time and the feedbacks built from the Jurdjevic-Quinn method. Numerical simulations show that the Jurdjevic-Quinn feedbacks can be close to the optimal command. In order to understand this property we study an average control system whose trajectories approximate these of low thrust systems. This technique allows us to give a positive answer to a conjecture on the asymptotic behavior of the minimum time. Moreover it is a promising way to build an efficient Lyapunov function associated to the Jurdjevic-Quinn method: a feedback close to the optimal control

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