On Controlling the Effect of Error Growth in Unlimited Encrypted Iterative Learning Control

What the math gives to ML

The paper identifies a nonstandard failure mode in encrypted iterative learning control: a closed-loop controller can suppress ciphertext perturbations, while marginally stable trial-to-trial ILC updates accumulate them without bound. Its constructive remedy is a range-space decomposition that removes update components which cannot affect the desired output trajectory, thereby preventing repeated injection of encryption noise into ineffective directions. The transferable neural-network mechanism is a projected, noise-aware update for repeated-horizon training or inference, where parameter updates are restricted to directions that change the model's observable outputs. The key testable prediction is that perturbation variance grows linearly with the number of iterations for the unprojected method but remains bounded or grows substantially more slowly after projection.