Introduction to Linear Quadratic Regulator (LQR) Control

In this video we introduce the linear quadratic regulator (LQR) controller. We show that an LQR controller is a full state feedback controller where the gain matrix K is computed by solving an optimization problem.

Topics and time stamps:

0:00 - Introduction
4:01 - Introduction to Optimization
19:24 - Setting up the cost function (Q and R matrices)
41:36 - Solving the Algebraic Ricatti Equation
1:01:05 - Example of LQR in Matlab
1:17:09 - Using LQR to address practical implementation issues with full state feedback controllers

In addition, some videos that may be helpful or relevant to the discussion at hand include:
-Introduction to Linear State Estimation (TBD)

The Matlab/Simulink files associated with this video are located at:

[MrHucker]

Awesome. I haven't stayed awake through a 90+ minute lecture this easily in years. Great job

[samuelayankoso]

You have practically taught LQR control in a memorable way. Thanks for sharing.

[seismicdna]

first time i felt even slightly comfortable with LQR after many videos. thank you so much professor!

[hetvivyas]

A single video gave me all the details to start with LQR. Thank you !!

[Dollyo]

Amazing video about LQR, really informative and I really like how you also show the practical implementation problems and how to approach them

[morganwalker]

You've done it again, Chris! Not only do I know more about LQR control, I now know a bunch of different ways to get to Bainbridge Island from here. I'll have to try them all out sometime!

[krystoflis]

I always enjoy a optimization discussion on commute especially when a helicopter is an option. Great introduction to optimization and LQR.

[vladimirzz]

I´ve seen three of your videos and I reckon each video was made with effort and in the best didactic way. I am grateful, they were a big help, thank you a lot. Cheers from Ecuador!!!

[justinhendrick]

I really appreciate the practical approach you take to teaching controls concepts. I'm glad we didn't go into the weeds of deriving the solution to an LQR optimization problem and instead focused on how to use LQR to tune a controller

[hanzyloeser]

I was a complete neophite in control theory until I stumbled on your videos and now I'm beggining to understand. They are great thanks

[everettkinyon]

I really enjoyed the detail about the LQR method, it's also great to see that Matlab has an built in function to use it.

[gitarplayer]

Thanks professor. I liked the examples, they made the concepts very clear and easy to understand from an engineering perspective rather than just the mathematical theory.

[mehmoodkhan]

I have never spent 3 hours on a video before...if by chance my brain started to think about some random things I kept rewinding it to watch it with full focus. gonna watch again tomorrow with a notebook to make notes so i can memorize the dialogues :D Thanks for the awesome clarification.

[selamhendrix]

Thank you for such a simple way of describing and visualizing what Q and R are and the real life example to really solidify how to use LQR.

[darylfishback-duran]

Great introduction to LQR! The examples that change Q and R help gain intuition as a controls engineer.

[darksideng]

Amazing!!! Than you professor!!!
Unbelievable how it is easy to understand when you explain...

[justforfun]

Hi Chris, thank you for putting the effort to make this lecture and having it online.

[tascker]

This is an honest to goodness very good lecture, I'm learning LQR best than in the books. Thanks a lot.

[bryceelliott]

Thanks for this. It has been a helpful introduction. I haven't had to deal with matrix control in more than 15 years, and I appreciate how you try to relate the math to the physical.

[rajabmur]

usually I don't like the idea of watching a video more than 15 minutes but honestly I watch all your videos until the end, you are great professor thank you so much