Mathematical genericity and engineering reality

Professor John Doyle, Control and Dynamical Systems/Elect. Eng., Caltech

This informal talk is primarily aimed at first-year CDS students taking CDS 112 and 140, although everyone is welcome to attend and even contribute to the discussion. In both classes, we spend substantial effort understanding the structure of problems that occur only on a thin set of systems (eg. nontrivial Jordan forms, nonhyperbolic, uncontrollable, unobservable,...). While they may be interesting mathematically, it could be argued that such exotica cannot possibly be very important for models of systems that arise naturally in science and engineering. We will see that exactly the opposite is true, that realistic models almost always have features which are highly nongeneric. We will avoid heavy mathematical machinery, but try to reconcile our mathematical intuition with our real-world experience.