This page indexes materials I found useful for familiarizing myself with new or otherwise challenging concepts. I hope they are useful to others as well.

Computational Motor Control for Neuroscience

Theory of Optimal Control

Optimal Control Systems

By D.S. Naidu

This textbook is a good starting point to learn about optimal control for people with less engineering experience. The first asset of this book is that it shows the maths only after explaining what we are trying to do, rather than before. Maths can be a bit of a scarecrow, but when we know what a formula is trying to achieve before we even get to it, it is usually easier to appreciate what it really represents.

The second asset of this book is that, well, it still shows the maths. Many books go at lengths trying to build a maths-free intuition for the concepts discussed and then just don't bother showing the math at all, under the logic that an intuitive understanding is already conveyed. While this is a reasonable logic, it also misses on a great opportunity to link the now-gained intuitive understanding to its mathematical formalization, which is also a worthy skill to developp.

The third asset of this book is its exercice section at the end of each chapter. They are very well crafted, reasonably progressive in difficulty, and overall a great mean of playing with newly acquired concepts.


Optimal Control and Estimation

By R.F. Stengel

Chapter 4 provides a well-laid explanation of Kalman filtering. It starts with a simple least-square extimator, then adds propagation over time of state estimate uncertainty to yield the Kalman filter. This is then followed by an extension to the continuous-time case (Kalman-Bucy filter) and non-linear case (extended Kalman-Bucy filter, Quasilinear Filter).


Lagrange Multipliers

This video provides an intuitive geometrical explanation of how Lagrange multipliers work for constrained optimization.


Imaginary Lateral numbers

Lateral numbers, better known as imaginary numbers, are somewhat mystifying because what they represent in real life seems difficult to grasp for the human mind. Who doesn't get a bit scared when their running code start returning 3 + 5i seemingly out of the blue? This 13-episodes (!) series breaks down what lateral numbers are, why it should be called lateral numbers rather than imaginary numbers, and more importantly, why they should be no more mystifying than, say, negative numbers.

Data Science

Support Vector Machines

This video provides a breakdown of the theoretical basis for support vector machines.