arXiv:2607.13513 2026 Dynamics 1 ideas extracted · analyzed Aug 30, 2026
The paper offers a transferable mechanism for safely switching between an adaptive performance controller and a saturated stabilizing controller under model uncertainty and unbounded disturbances. Its key construction is hysteresis switching: the fallback controller is entered at one threshold and exited only at a lower threshold, preventing chattering and preserving continuity with respect to estimation errors. The paper also propagates finite-time parameter uncertainty through the control law using a Lipschitz sensitivity bound. A neural-network analogue is a safeguarded optimizer that uses a learned update when a Lyapunov-like energy decreases reliably and switches to a contractive bounded update when uncertainty indicates possible instability.
Use a two-mode optimizer: a learned preconditioned update for normal training and a bounded contractive fallback when the learned update is predicted to increase a monitored energy. Use separate entry and exit thresholds so minibatch noise does not cause rapid switching.