Robust and efficient data-driven predictive control

Abstract

We propose a robust and efficient data-driven predictive control (eDDPC) scheme which is more sample efficient (requires less offline data) compared to existing schemes, and is also computationally efficient. This scheme employs a recently proposed data-based representation of linear time-invariant (LTI) systems as a predictor. Such a representation serves as an alternative to Hankel-based predictors obtained from, e.g., the so-called fundamental lemma, and can be derived by exploiting the kernel structure of shallow Hankel matrices of data. This allows for application of our proposed scheme using very short (and potentially irregularly measured) noisy input-output data, the amount of which is independent of the prediction horizon. To account for measurement noise, we provide a novel result that quantifies the uncertainty between the true (unknown) restricted behavior of the system and the estimated one from noisy data. Furthermore, we show that the robust eDDPC scheme is recursively feasible and that the resulting closed-loop system is practically exponentially stable. Finally, we compare the performance of this scheme to existing ones on a case study of a four tank system.