Data-Driven Synthesis of Robust Positively Invariant Sets: From State Feedback to Output Feedback

What the math gives to ML

The paper provides a constructive mechanism for synthesizing robust positively invariant ellipsoids directly from noisy input-state-output data, jointly with stabilizing feedback or observer gains, without first identifying an explicit plant uncertainty set. The transferable asset is an SDP-checkable certificate that bounded disturbances remain inside a bounded state region under closed-loop dynamics. A neural-network analogue is to treat recurrent hidden states as a controlled dynamical system and learn or constrain a hidden-state ellipsoid that remains invariant under bounded feature inputs, hidden-state perturbations, and model mismatch estimated from offline trajectories. This yields a falsifiable long-horizon stability condition rather than relying only on gradient or benchmark behavior.