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# A data-driven Riccati equation

*Proceedings of the 6th Annual Learning for Dynamics & Control Conference*, PMLR 242:504-513, 2024.

#### Abstract

Certainty equivalence adaptive controllers are analysed using a “data-driven Riccati equation”, corresponding to the model-free Bellman equation used in Q-learning. The equation depends quadratically on data correlation matrices. This makes it possible to derive simple sufficient conditions for stability and robustness to unmodeled dynamics in adaptive systems. The paper is concluded by short remarks on how the bounds can be used to quantify the interplay between excitation levels and robustness.