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Unsolved Problems in Mathematical Systems and Control Theory by Vincent D. Blondel, Alexandre Megretski

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Problem 3.1

Minimum time control of the Kepler

equation

Jean-Baptiste Caillau, Joseph Gergaud,

and Joseph Noailles

ENSEEIHT-IRIT, UMR CNRS 5505

2 rue Camichel

F-31071 Toulouse

France

{caillau, gergaud, jnoaille}@enseeiht.fr

1 DESCRIPTION OF THE PROBLEM

17135

Our first concern is uniqueness (see §3 about existence):

Question 1. Is the optimal control unique?

The second point is about regularity, namely:

Question 2. Are there continuous optimal controls?

Denoting by T(17153) the value function that assigns to any strictly positive (parameter involved in (4)) ...

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