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Optimal control and the geometry of integrable systems

Presented by: 
Anthony Bloch University of Michigan
Date: 
Wednesday 31st July 2019 - 15:00 to 16:00
Venue: 
INI Seminar Room 2
Abstract: 

In this talk we discuss a geometric approach to certain optimal control
problems and discuss the relationship of the solutions of these problem
to some classical integrable dynamical systems and their generalizations.
We consider the
so-called Clebsch optimal control problem and its relationship
to Lie group actions on manifolds. The integrable systems discussed include
the rigid body equations, geodesic flows on the ellipsoid, flows
on Stiefel manifolds, and the Toda lattice
flows. We discuss the Hamiltonian structure of these systems and relate
our work to some work of Moser. We also discuss the link to discrete dynamics
and symplectic integration.


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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons