Quadratic Regularization of Data-Enabled Predictive Control: Theory and Application to Power Converter Experiments

Bridging direct & indirect data-driven control formulations via regularizations and relaxations

“…We illustrate our results with numerical studies illustrating the role of regularization, superiority of the new regularizer, and comparisons. Informed by our analysis, we hypothesize and numerically confirm that the indirect approach is superior in case of "variance" error, e.g., for LTI stochastic systems, and the direct approach wins in terms of "bias" error, e.g., for nonlinear systems supporting the observations in [35]- [38].…”

“…To go beyond certainty equivalence, [30]- [35] reformulate the constraint in (6) as col(w ini , w) = H Tini+L (w d )g for some g and robustify problem ( 6) by means of regularization:…”

“…The regularization function h(•) and parameter λ are nonnegative. Choices for h(•) are one-norms [31], two-norms [34], squared two-norms [30], [35], or arbitrary p-norms [32], [33].…”

“…The regularizers can be related to min-max optimization formulations either in deterministic [34], [35] or stochastic contexts [32], [33]. For instance, if one seeks robustness with respect to all distributions that could have generated the data w d within a p-Wasserstein ball centered around the empirical distribution, then one has to (i) regularize with the dual norm h(g) = g * p and (ii) choose λ ≥ 0 as the radius of the Wasserstein ball times the Lipschitz constant of c ctrl (•) [32], [33].…”

“…The regularizations were first mere heuristics [31] but have later been constructively derived by robust control and optimization [32]- [35]. These approaches, albeit recent, have proved themselves in practical nonlinear problems [35]- [38]. We also note the recent maximum-likelihood perspective [39].…”