A Lecture Series That Shaped How I Understand Optimal Control

As I started my Ph.D. and began working under Prof. James T. Allison on control co-design problems, it quickly became clear that optimal control is a foundational topic for anyone working at the intersection of dynamics, control, and optimization. After searching for high-quality learning resources, I came across a full lecture series from EML 6934: Optimal Control (Spring 2012), taught by Prof. Anil V. Rao at the University of Florida. I initially started watching the lectures out of curiosity, but very quickly realized how exceptional they were. The material is rigorous, carefully structured, and presented with remarkable clarity, especially given the mathematical depth of the subject.

I ended up watching all of the lectures and took extensive notes in just four to five days. The way Prof. Rao builds intuition, connects theory to numerical methods, and repeatedly reinforces key ideas made the concepts stick in a way that textbooks alone never had for me. His enthusiasm for teaching and for the subject itself is evident throughout the entire series.

Following the lectures, I also worked with GPOPS-II, a software package for solving optimal control problems developed by Prof. Rao’s team. Having a strong theoretical foundation made the implementation aspects much more intuitive. Concepts such as transcription methods, collocation, and constraint handling suddenly became practical tools rather than abstract ideas, and I found the workflow both powerful and efficient.

What impressed me most is the care and intention behind the course design. The clarity of the explanations, the pacing, and the emphasis on understanding rather than memorization are outstanding. I still revisit parts of this lecture series, and I actively try to incorporate elements of Prof. Rao’s teaching approach into my own lectures and mentoring whenever I cover optimization or control-related topics.

For anyone learning or teaching optimal control, this lecture series is an invaluable resource and well worth the time investment.

You can find the full lecture playlist here:
https://www.youtube.com/playlist?list=PLIygTcviGPKBCJ9JyHfBi4ftc9FDCtaBc