Lifting as an abstraction

For control synthesis for cyber-physical systems, it is common to create a discrete abstraction that satisfies a simulation relation with the original system. When working with discrete systems, going from a larger discrete system to a small one via abstraction simplifies the problem. However, when working with continuous systems one can also simplify the dynamics by lifting to a large dimensional (yet linear) system. This is in a sense similar to Kernel embeddings in machine learning. This talk will summarize some of our initial investigations in this direction, how such liftings can be used for synthesis of controllers, and how it is related to Koopman embeddings. I would also be interested in hearing participants perspectives on whether such lifting ideas exist in discrete reactive systems or software synthesis.