Optimization and Systems Theory Seminar

November 19, 15.30-16.30

Professor Hector Sussmann
Department of Mathematics,
Rutgers University,
New Brunswick,
USA.

Lie brackets and impulse controls

We show how the concept of an impulse control, for systems involving noncommuting vector fields, cannot be made meaningful by using Stieltjes integrals or distibutional controls. We proposed instead to use time-reparametrizations and graph-completions, in the spirit of the work of A. Bressan and F. Rampazzo. By means of some simple optimal control problems, we show how the optimization problem truly requires these more general notions, since different problems can have truly different solutions, all of which agree as distributions.