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.
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.
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.
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.