Floodgates up to contain the DeePC and limit extrapolation

TL;DR

This paper proposes an approach to slow down the distributional shifts and therefore enhance the safety of the data-enabled methods by introducing quadratic regularization terms to the data-enabled predictive control formulations.

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.

Figures (1)

• Figure 1: X-axis and y-axis correspond to the state space, $x_{1,k}$ and $x_{2,k}$, respectively. The blue circles are the (hidden) state data corresponding to the initial simulation experiment, using $u_k=K_0 y_k$. The orange diamonds are the state data resulting from solving Problem \ref{['prob:Data-conforming DeePC']} with $\gamma=5$, showing a similarity in state distribution to that of the collected data. The green squares are the states resulting from using the regular DeePC algorithm, Problem \ref{['prob:Standard DeePC']} (or, equivalently, Problem \ref{['prob:Data-conforming DeePC']} with $\gamma=0$), and only few of these squares are shown as the system has gone unstable after few time-steps.