Floodgates up to contain the DeePC and limit extrapolation

TL;DR

This paper introduces quadratic regularization to behavioral data-enabled control methods to slow distributional shifts, aiming to improve safety by reducing extrapolation risks at the cost of exploration.

Contribution

It proposes a novel regularization approach to mitigate distributional shifts in data-driven control, enhancing safety in systems with linear assumptions.

Findings

Regularization reduces distributional shifts in control systems.

Trade-off between exploration and safety is demonstrated.

Enhanced safety in control with minimal performance loss.

Abstract

Behavioral data-enabled control approaches typically assume data-generating systems of linear dynamics. This may result in false generalization if the newly designed closed-loop system results in input-output distributional shifts beyond learning data. These shifts may compromise safety by activating harmful nonlinearities in the data-generating system not experienced previously in the data and/or not captured by the linearity assumption inherent in these approaches. This paper proposes an approach to slow down the distributional shifts and therefore enhance the safety of the data-enabled methods. This is achieved by introducing quadratic regularization terms to the data-enabled predictive control formulations. Slowing down the distributional shifts comes at the expense of slowing down the exploration, in a trade-off resembling the exploration vs exploitation balance in machine learning.