Generalize the stochastic DPC framework to correlated or conditionally independent disturbances

Develop an extension of the proposed stochastic data-driven predictive control framework for linear systems with autoregressive disturbance models to cases in which the aggregate disturbances are correlated or conditionally independent, potentially by exploiting the corresponding results of Ao et al. on sub-Gaussian disturbances.

Background

The paper’s main framework assumes that the additive disturbances in the ARX system are independent and identically distributed sub-Gaussian random variables. The discussion considers a more general disturbance model in which each aggregate disturbance depends on autoregressive terms of an underlying disturbance sequence. In that setting, even if the underlying disturbances are sub-Gaussian, the aggregate disturbances may no longer be independent. The authors note that existing results could potentially support a generalization to correlated or conditionally independent disturbances, but leave the required detailed analysis unresolved.