[pidtuner]

The problem with many adaptive control techniques is that is very difficult to prove the closed loop stability and performance margins, because such systems are highly nonlinear and we do not have yet the mathematics to provide simple guarantees (for example, I would not get into an aircraft where the control systems have not been rigorously, mathematically, designed)

The integral problem of LQR and MPC is indeed not the first topic discussed on textbooks, but there has been a solution for that for year, called "disturbance model". You you can have an "adaptive MPC" following some design procedures. Check out this reference:

https://folk.ntnu.no/skoge/prost/proceedings/ifac2014/media/...

[gugagore]

Thanks for the reference. I agree that the solution to getting I action is to model the disturbance, and augment the state. The system certainly becomes uncontrollable in the augmented state space.

I've run into a conceptual problem when using this approach with [infinite-horizon] LQR to try to recover what looks like a PID controller, which IIRC is due to the control u not necessarily converging to 0. This is expected, to counteract a constant disturbance, but it means that the sum doesn't converge.

I only skimmed the reference, but I did not find a discussion of this issue.

[pidtuner]

The trick is that, even though the augmented state is uncontrollable, you still use it in the predictions, so the MPC algorithm can still compensate for it. Take a look at the before-last graph in the paper, see how that technique improves predictions after learning the real-time disturbances.

[gugagore]

That's not what I was concerned about. The subspace that's uncontrollable is the disturbance components of the state, which I don't care to control anyway.

[pidtuner]

Not to control, but to compensate. This is what the I action in the PID does, compensate for un-modeled disturbances