Causality-Informed Data-Driven Predictive Control

Abstract: As a useful and efficient alternative to generic model-based control scheme, data-driven predictive control is subject to bias-variance trade-off and is known to not perform desirably in face of uncertainty. Through the connection between direct data-driven control and subspace predictive control, we gain insight into the reason being the lack of causality as a main cause for high variance of implicit prediction. In this article, we seek to address this deficiency by devising a novel causality-informed formulation of direct data-driven control. Built upon LQ factorization, an equivalent two-stage reformulation of regularized data-driven control is first derived, which bears clearer interpretability and a lower complexity than generic forms. This paves the way for deriving a two-stage causality-informed formulation of data-driven predictive control, as well as a regularized form that balances between control cost minimization and implicit identification of multi-step predictor. Since it only calls for block-triangularization of a submatrix in LQ factorization, the new causality-informed formulation comes at no excess cost as compared to generic ones. Its efficacy is investigated based on numerical examples and application to model-free control of a simulated industrial heating furnace. Empirical results corroborate that the proposed method yields obvious performance improvement over existing formulations in handling stochastic noise and process nonlinearity.