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Special Lectures

Geometric Optimal Control with Applications II(G30:Special Lectures IV)

Hold Date
2015-07-01 16:40~2015-07-13 16:20
Place
Seminar Room 7, Faculty of Mathematics building / IMI, Ito Campus
Object person
Students who take an interest in this lecture 
Speaker
Bernard Bonnard (Université de Bourgogne)

Abstract:
In the firrst part of the class, various applications of the maximum principle will be explored, in particular the time minimal problem and the linear quadratic optimal control case. Higher order conditions with the concept of conjugate point will be introduced, and an introduction to numerical methods will be given. Then, optimal control theory will then be used to answer purely geometric questions, in particular to study extremals in sub-Riemannian geometry and the role of the so-called abnormal geodesics. The second part
of the course will be devoted to analyzing two specific applications. First, a new approach to the contrast imaging problem using tools from geometric optimal control will be explored. The problem is to bring one spin the origin of the Bloch Ball while maximizing the square of the norm of the magnetization vector for the second spin. The optimal solution can be found as an extremal, solution of the Maximum Principle
and analyzed with the techniques of geometric control. This leads to a numerical investigation based on so-called indirect methods. Second, we will focus on geometric and numerical techniques to study the orbit transfer between Keplerian elliptic orbits in the two-body problem or between quasi-Keplerian orbits in the Earth-Moon transfer when low propulsion is used.

Date:
July 1 (Wed) 16:40-18:10
July 2 (Thu) 16:40-18:10
July 6 (Mon) 13:00-18:10
July 8 (Wed) 16:40-18:10
July 9 (Thu) 16:40-18:10
July 13 (Mon) 13:00-16:20