Theory of Input Driven Dynamical Systems

Most dynamic models of interest in machine learning, robotics, AI or cognitive science are nonautonomous and input-driven. In the last few years number of important innovations have occurred in mathematical research on nonautonomous systems. In understanding the long term behavior of nonautonomous systems, the notion of an attractor is fundamental. With a time varying input, it turns out that for a notion of an attractor to be useful, the attractor cannot a single subset, but must be conceived as a sequence of sets varying with time as well. The aim of this tutorial is to illuminate useful notions of attractors of nonautonomous systems, and also introduce some newly emerging concepts of dynamical systems theory which are particularly relevant for input driven systems.