I wish I could upvote this twice. This is the best basic introduction to concepts in functional analysis that I've seen. Another great overview that goes deeper

I wish I could upvote this twice. This is the best basic introduction to concepts in functional analysis that I've seen. Another great overview that goes deeper into the math is [1]. Another fantastic application that the website doesn't mention is the composition / Koopman operator. In control theory (e.g. autonomous drones, cars, robot arms, etc.), most real-world systems are described by nonlinear dynamics which are very difficult to work with (e.g. safety/stability guarantees, optimizing over forward horizons using NMPC, state estimation, etc.) The Koopman operator however gives a globally relevant linear approximation of non-linear systems. In other words, you can treat a nonlinear system as a linear system with fairly high accuracy. This greatly simplifies control and estimation from a computational perspective. You can also learn these linearizations from data. Steve Brunton has some good materials on Koopman theory [2][3], and there are some great applications to control of systems such as soft robots [4]. [1]: https://arxiv.org/abs/1904.02539 https://arxiv.org/abs/1904.02539 [2]: https://youtube.com/playlist?list=PLMrJAkhIeNNSVXUvppZTYNHKQUD-oWys9 https://youtube.com/playlist?list=PLMrJAkhIeNNSVXUvppZTYNHKQ... [3]: https://arxiv.org/abs/2102.12086 https://arxiv.org/abs/2102.12086 [4]: https://arxiv.org/abs/1902.02827 https://arxiv.org/abs/1902.02827