The notions of potential (going back at least to Lagrange) and that of controllability (due to Kalman) are fundamental in engineering. At first glance, there does not seem to be any connection between the two. It is through the reformulation of control theory due to J.C. Willems (the theory of behaviours) that we realise that they are intimately connected, and it turns out that a system that admits a potential is always controllable. A question remains: does a controllable system always admit a potential? In this talk I shall examine the evidence.
Shiva Shankar works at the Chennai Mathematical Institute. A lot of the subject matter of this talk was worked out in collaboration with Harish Pillai (when the former was at the EE dept. at IIT Bombay and the latter a Ph.D. student).