Model Predictive Control - Part 2: Numerical Methods for MPC (Lasse Peters)

[@1volkansezer]

Very nice wrap-up, thank you Lasse!

[@hasinabrar3263]

This is brilliant, You sir is a legend.

[@mathiaswittig5249]

Tanks for those 2 videos!

[@andreasteriete5616]

Thanks for these lectures. What I don't understand is part of you motivation to use Dynamic Programming LQR to speed up the calculation of the inverse of the H matrix. Are you really interested in the inverse of the H matrix or do you simply need the solution of the linear system, which is way easier to compute?

[@vivekbagaria3324]

Thanks for the explanation. It was crystal clear!

[@xuanchenzhang1056]

would you give lectures about solving NMPC by SQP and IP？

[@e55c63]

amazing explanation!

[@tejasstanley]

Hallo, are the slides for this lecture available online.

[@CyrillStachniss]

Yes they are. Send ma an email

[@kaiscott8345]

Is there any PPT of this course to download? Thanks

[@1volkansezer]

I would like to ask, where did we consider the input and state constraints (u is an element of U; x is an element of X), during both batch LQR and DP-LQR solutions? Both of the are based on LQR optimization which does not consider these constraints; or I am missing something :).

[@lassepe]

Thank you for the question. As pointed out around 6:35, for the scope of this lecture we do not consider state and input constraints. Thus, with the tools developed here you would have to encode these as soft constraints as part of the cost (e.g. penalize states outside X and inputs outside U). If you are interested in learning more about how to explicitly incorporate constraints in this framework, I recommend reading Chapter 17 and 18 of "Numerical Optimization" by Nocedal and Wright. There exist various methods for applying these ideas to the very framework of iLQR; for example [this paper](bjack205.github.io/papers/AL_iLQR_Tutorial.pdf) discusses Augmented Lagrangian methods for incorporating constraints in the framework presented in this lecture.

[@1volkansezer]

Thank you for this clear answer. I thought that it was just a temporary simplification and we would see how to consider those constraints somewhere in the video. Since one of the most critical advantages of MPC over LQR is taking into account of those constraints, a Part-3 video would be perfect to complete the series; in order to illustrate how those constraints are handled in MPC. And thank you very much again for this nice wrap-up.

[@userjdufer466]

nice!

[@sarveshgaonkar7507]

Did anyone tried getting the Reformulated J after substituting the X = Axinit + Bu in the cost function. Its different when i tried, the term 2xinitFU doesnt is little different

[@mohamedgbreel8618]

awesome!

[@yormanjorcetquispechavez3330]

Subtitules please 😭😭😭🙏🙏