I'll think I'm gonna re-watch this playlist in a few weeks. So many insights and so great to follow. Thank you a hundred times.

Finally I made it to the last lecture of this series! After some revision I will start the Data-Driven Dynamical Systems with Machine Learning series. Thank you so much Steve!

Your lectures on dynamic systems, advanced solution techniques for PDE's, and control theory have been a goldmine for me, I discovered your channel 3 days ago and have watched in excess of 12 hours of your content since then. I'm a junior, and my goal this summer is to move the eigenvalues of my dynamic systems competence matrix to the Right half plane in SU3

Thank you for this video. Made a complex topic really easy to understand.

Wow Steve. Your channel is incredible. I am a ME student at Purdue, and I love learning these kinds of things. I have learned so much from your channel! Thank you!

You have presented a good and to-the-point introduction of MPC...

This is the first lecture on MPC that I have seen that actually made sense to me and allowed me to understand what MPC is. The previous ones I attended were a soup of symbols and jargon with no meaning to me. Thank you so much.

Thank you so much. I have been wondering what it was for a while. In 10 minutes you explained it very well. Its much easier to understand the the basic idea behind the concepts concepts from your videos than from papers/books.

best video on MPC period.

Simple modeling , but the point what we should understand this complex environements. You are brave . thanks a lot.

Brilliantly explained!!. and I'm looking forward to your lecture on Markov decision process. I'm working on implementing a hybrid controller by combining the benefits of both MPC and Markov Decision Process. I hope this hybrid controller would be more efficient in terms of computational time!!

Thank you! My prof can't explain it as well as you. Saving me a part of my exam on friday :D

I have been seen your lecture since I admitted in my master course of autonomous vehicles engineering. After a some time ,wish to do PhD under you!

Thank you for your videos! Are there any stability guarantees when using MPC on nonlinear systems?

Really well explained!

what a fantastic explanation! Thanks

Great explanation! Thank you!

thank you for this amazing lecture series. please make more videos about model predictor controll.

Great video! I appreciate that very much.

great video steve, thanks!

This reminds me of some reinforcement learning ideas related to adjusting input in real-time. interesting!

You are writing backwards, reading it backwards, and still explaining things clearly... well done and thank you.

Dear professor, I am working on fuel cell control and optimization, I am interested in MPC , how to start ? Moreover if I simulate a fuel cell and extract input output data for MPC will be a valid case ? Mostly MPC needs experimental data . Little confused . Need your kind help

Great video Steve! Does anyone have a suggestion for creating a system model to use with MPC? I have a large amount of historical data for a mechanical vapor recompression system.

Hi Sir! Thank you for this valuable splendid axplanation. Could there be an example from you or are there any sources to look for impelementing?

You have nicely explained a complex topic. I've designed an MPC controller for a power converter. But don't know how to tune the controller. Because the variation in the load affects it's performance. Could you please suggest something regarding this?

Nicely explained. Inspirirng, thankyou

Great explanation

Thank you for the amazing video on this topic. I am interested in adding stochasticity to nonlinear MPC, can you please refer me to some references on this topic?

Liked the lecture. Thank you sir.

Great video, great as always :) However, I am missing the important point, that *if* we need to take constraints into account, we can't use an LQR since it controls an unconstrained system to a zero state, this is why we need to implement a MPC. Thanks again for your videos!

Hello professor! Could you explain invariant sets and maximal control invariant sets? I'm having trouble grasping the concept.

So, 5 years ago this was your last video about MPC under "Control Bootcamp" series. So unfortunately, MPC stopped here with Professor Steve! Anyway, thank you for the clear explanation.

Great lecture. I am wondering if you are using the same computation device to measure the signal, as well as generate the optimal best path, then could there be a tradeoff for re-calculating the optimal trajectory at every step? Or for too many steps ahead of time at?

great video!

Steve, thank you for the great lecture series. You'll be happy to know that people are still sitting down and watching the whole series. I've seen you answer relatively recent comments in some other video, so if you see this, since you mention a number of times where you would make your students prove an equation or another, I was wondering at what level of learning you'd place the material in this bootcamp? I'm a PhD candidate in Wind Engineering so I have pretty much no background in control engineering, and it was easy enough to follow, but I know that this would have been incomprehensible for me just a few years ago. For software or mechanical engineers, would this material be covered in undergrad? Or are these graduate-level concepts?

Thank a lot for this video. Really easy to understand and looking forward to future videos. Would you be making any videos on deep learning for MPCs or differentiable MPCs?

Thank you for this introduction! I hope there will be more videos on MPC in the future. What book do you recommend for MPC beginners?

Thanks for the lecture professor. I have one question could you please clarify? around 2:45, I thought the first control at k+1 we locked in should be applied to system at k+1, not at k in the above plot -- because at initial time k, Xk is given to calculate (by optimization) the controls of Uk(not useful), Uk+1, Uk+2, etc to minimize the objective within prediction horizon, but the optimization takes time, it's only practically to apply Uk+1 to system at k+1, not at k. Similarly, at k+1, Xk+1 is known, and Uk+1(calculated at k) is applied to the system, and Uk+2 is to be calculated. This process repeats.

@Steve Brunton Suppose we have a nonlinear dynamics and obtained a linear representation by Koopman operator. Is it ok to apply to Koopman linear representation? If it's ok , which is more reliable? linearize on equilibrium point or koopman?

Can you use information about the deviations of predicted output compared to eventually measured output to improve the model over time to reduce disturbances (mainly caused by model inaccuracies)?

hi... can I know what is the difference between model based control and model predictive control?? and is the model-based is one approach like Zigler and Niglust??

Does the optimal control signal have to be a step function?

Dear Dr Steve Brunton,,why didn't you explain this superb explanation (by you ) on MATLAB?

Is MPC a feedback control?

what action will the mpc take when reached setpoint

Lateral inverted writing skill. Wow!

Thank you for the helpful explanation. But I have two questions: 1) Let's say I'm controlling the speed of a motor, which is running a variable load. In the model, the load is considered a disturbance and is not included in the differential equations. So, if for example, the load is suddenly removed from the motor, the speed will increase quickly. How can this optimization compensate for such disturbances if they are not included in the models. PI controllers can compensate that because their outputs are dependent on the error signal. 2) How is this optimization carried out?

This remind me about adaptive control. Of course for adaptive gains.

Great!

Could you please also upload a detailed video lecture on MPC? Your Control Boot Camp lectures are very useful in revising and honing the fundamental concepts in Control Systems Engineering.

Can we apply the MPC for a model to predict its parameter online , not for control system but just to identify the non linear model .

I work in MPC for autonomous cars... Things will always be easy and smooth in simulation... Closed loop on real time platform is where i m facing the heat....😬 That is why i love control systems ..✌️

what I dont understand is why one need output constraints especially soft ones since we have anyways the set value?

I want to ask, why do I need to calculate the horizon, if I only ever need the first point of that horizon ?

Learning Neural Weights + update Inference on the fly. I wonder if Tesla is already doing this for updating their Autopilot with edge cases?!

Two questions: - Why do we bother optimizing over the entire horizon when only the t+1 step is necessary? Unless the optimization solution is generated starting from the end of the horizon backwards. - Does it often happen nowadays to have real-time systems running their optimizations over the air on a powerful backend (cloud),. What types of systems are suitable given the network latencies of doing so?

Why we apply only the first control input proposed by the optimizer istead of using all the controls.

Hey Steve, I have a doubt about the process. A horizon is chosen, a minimization is made similar to the LQR of a time t_0 to a time t_f, and a value of K is calculated. This K, with u = -Kx, is applied and the state is calculated. In the next iteration, the new information is added to the model, so that the new K is calculated, which may be different from the previous one. Again, this u = -Kx control law is implemented. Is that the logic of the process? In general, is it like to use the LQR for each iteration? So that, if nothing in the model changes, would we have an equal K in each iteration and the process would be nothing more than an LQR?

very good video! thanks!!!

I don't understand. Isn't k equal to time t? What does k+1 imply ? Is it the shift of the time horizon?

thanks

Is MPC a numerical command?

Where is the continuation of this video?

sir which paper you have referenced in this?

okay now where do you use it

Thanks for this video ! Could you perhaps do a video of a matlab example of application of MPC on a linear model of system identification ? In practice, we usually only have data measurement of a system so both A and B are unknown in our model. Would be great to do a full example considering this. Thanks for your work !

has anyone noticed that steve draws mirror images of everything he's explaining or am i wrong? just curious because i think its amazing !!

I love the backward-writing skills!

the "set goal" unfortunately IS to have "control" over Time. that's where our problems begin. but denying it won't change the equation.

All these comments and none of them mention how well he writes backwards.

bruh. How do I like this video twice? For anyone who didn't realize, he's writing backwards.

Shrill sounds when you write

Is this guy writing backwards??

get some new pens

nice backward writing skills. MATLAB had a video on this and it is more detailed.

Did you train yourself to write backwards?