Abstract:
Bilinear control systems are receiving increasing attention in recent years, as they can be used to study problems for which an additive control action would be unrealistic. For such systems, in infinite dimension, weaker controllability properties can be expected than for systems with additive controls. For instance, exact controllability is out of question due to a well-known negative result by Ball, Marsden, and Slemrod back in the 80’s. Nevertheless, one can seek to steer states to special targets either in finite or infinite time. In this talk, I will present recent results where the above problem is addressed for evolution equations of the form u'(t) = Au(t) + p(t)Bu(t), with A a self-adjoint negative operator on a Hilbert space, B a linear operator satisfying a certain spreading condition, and p(t) a single-input control. When such a condition fails for B (for instance when B=I), I will also discuss control issues that can be reduced to invariance problems.
The seminar will be held in the Mail Lecture Hall and it will also be streamed online via zoom at this link:
https://us02web.zoom.us/j/83520111787
Please notice that, in accordance to GSSI regulations, your Green Pass will be checked at the entrance.