Adjustment formulas for learning causal steady-state models from closed-loop operational data

Steady-state models which have been learned from historical operational data may be unfit for model-based optimization unless correlations in the training data which are introduced by control are accounted for. Using recent results from work on structural dynamical causal models, we derive a formula for adjusting for this control confounding, enabling the estimation of a causal steady-state model from closed-loop steady-state data. The formula assumes that the available data have been gathered under some fixed control law. It works by estimating and taking into account the disturbance which the controller is trying to counteract, and enables learning from data gathered under both feedforward and feedback control.