Robust Data-Driven Safe Policy Update with Lyapunov Stability Guarantees

This paper presents a robust data-driven policy-update method for discrete-time linear quadratic regulation of unknown linear systems affected by bounded data disturbances. Input–state measurements define the set of dynamics consistent with the data, and state-feedback controllers are updated without identifying a nominal model. Each controller update is certified by a common quadratic Lyapunov function obtained from linear matrix inequalities derived through data-based elimination of the system matrices and Petersen’s lemma. A proximal redesign term centered at the current controller links consecutive controllers and yields a convex update for a fixed Petersen multiplier. The resulting procedure generates a sequence of controllers and returns a final controller Kf whose robust closed-loop stability is verified over the entire data-consistent model set. Closed-loop tests on a low-dimensional random test suite illustrate how the certified data-driven controllers empirically approach the model-based LQR performance computed on the true validation model, compare against one-shot and identification-based baselines, and include a proximal-term ablation.