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.

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.

Yes they are. Send ma an email