Kalman's fundamental notion of a controllable state space system, first
described in Moscow, has been generalised to higher order systems by Willems, and further to distributed systems de ned by partial di erential equations .
It turns out, that for systems de ned in several important spaces of distributions,
controllability is now identical to the notion of vector potential in physics, or of
vanishing homology in mathematics. These lectures will explain this relationship,
and a few of its consequences. It will also pose an important question: does a
controllable system, in any space of distributions, always admit a vector potential?
In other words, is Kalman's notion of a controllable system, suitably generalised,
nothing more or less than the possibility of describing the dynamics of the
system by means of a vector potential?
Financial support:
The visit of Shiva Shankar is supported by the Simons Foundation (grant No. 615793).
Organizer