A New Approach for Feedback Stabilization and its Application for Data-Driven Control of Polynomial Systems

What the math gives to ML

The paper develops data-driven feedback-stabilization conditions that certify a controller against an entire uncertainty set of plants consistent with noisy measurements, rather than only against a fitted model. The transferable asset is the combination of an explicit matrix-ellipsoidal model set with Lyapunov/dissipativity inequalities enforced through SOS optimization. A practical neural-network adaptation is to train a state-feedback MLP or neural ODE controller with a sampled robust Lyapunov-difference penalty, where uncertain plant matrices are drawn or optimized from the data-derived ellipsoid. This gives a falsifiable route to improved closed-loop stability under model error, although exact SOS certification is likely limited to low-dimensional polynomial surrogates.