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

This paper proposes a Ring Learning With Errors (Ring-LWE) based encrypted iterative learning control (ILC) framework for repetitive tracking tasks over networked control systems. The architecture integrates an encrypted dynamic feedback controller with an encrypted ILC computation. During each trial, the feedback controller is evaluated in the ciphertext domain, and the encrypted output trajectory is stored directly in the cloud. After each trial, the cloud evaluates the tracking error and performs the ILC computation from the stored ciphertexts, so that the plant side does not need to store the accumulated trial data. The proposed framework uses distinct packing parameters for ciphertext multiplication, allowing the cloud to handle both lower-dimensional output feedback control and higher-dimensional ILC computation without decryption. While error growth in Ring-LWE based encrypted control is generally suppressed by closed-loop stability, the marginally stable ILC iterations cause the injected errors to accumulate continuously. To address this challenge, a range-space decomposition is introduced in the encrypted ILC formulation to allow evaluation under unlimited updates. Numerical simulations show that the range-space decomposition suppresses encryption-induced perturbation, while ciphertext packing improves the computational efficiency of the encrypted ILC update.