Towards a unifying framework for data-driven predictive control with quadratic regularization
Manuel Klädtke, Moritz Schulze Darup
TL;DR
The paper addresses fragmentation among data-driven predictive control (DPC) frameworks by formalizing how DeePC and $\gamma$-DDPC relate under quadratic regularization. It shows that regularization in DeePC can be precisely mapped to $\gamma$-DDPC via an LQ-based coordinate transformation, and vice versa, enabling seamless transfer of theoretical results and insights. The key contribution is a set of equivalence propositions that connect specific regularization choices across frameworks, including standard $\|a\|_2^2$ and projection-based $\|\Pi_\perp a\|^2$, as well as their $\gamma$-DDPC counterparts. This unifying perspective clarifies how SPC-like predictors and exploration-exploitation trade-offs emerge in both formalisms, and suggests practical paths for framework unification and cross-pollination of results. The work paves the way for broader consolidation of DPC methodologies by focusing on structural equivalences rather than framework-specific formulations.
Abstract
Data-driven predictive control (DPC) has recently gained popularity as an alternative to model predictive control (MPC). Amidst the surge in proposed DPC frameworks, upon closer inspection, many of these frameworks are more closely related (or perhaps even equivalent) to each other than it may first appear. We argue for a more formal characterization of these relationships so that results can be freely transferred from one framework to another, rather than being uniquely attributed to a particular framework. We demonstrate this idea by examining the connection between $γ$-DDPC and the original DeePC formulation.