Here is a place for me to log random things for my personal use
I accidentally got into Dynamics & Controls and then rest is history. Control theory is very close to understanding and navigating the world around us. Our world is made up of space and time. All we are trying to do (as most engineers & scientists) is to reason how the world works and how can we plan our action to make the world work in the way we want.
This seems hard to understand but let me break it up here. We know that a wheel rotates when it is given some initial force. If we can control how it rotates (and other properties), we can make it do whatever we want - to build a race car/ railway carriage/ a bicycle. But this has taken some hundreds and hundreds of years before we moved from understanding the world and trying to make it work in a way we want. I hope this example quite captures my line of thought.
What is new about this now?
Historically, people tried to observe the patterns of the world, come up with a hypothesis and then try to prove them through analytical approach. It worked so well and the result is our current civilization. But we have now grown into a massive compute wealthy population that ever lived on earth (we can claim for lack of evidence). This has pushed our limits to model the world directly from data instead of going through hypothesis & proofs. As long as the models are accurate enough to our knowledge, we can then do many things using it - especially controlling it. This has sprung into many new fields and applications in past decade and I am not sure where we would be by the end of next decade. The growth is exponential, fascinating & sometimes thrilling.
Through this log website, I try to capture many fundamental theorems related to Information theory, Control theory, Estimation theory, Optimization etc. such that I can relate and learn how they all help to appreciate, model and act in the world around us. I am organizing my logs into Fundas (for fundamentals - evergreen theorems which you cannot miss), Thought logs (how I think about certain concepts), Side hustles (my experiments while learning new things) and Resources (for my future self to refer).
Join me in this journey !