ENClose: Encrypted Nonlinear Closed-Loop Control Over Fully Homomorphic Encryption

This work proposes an encrypted controller framework for closed-loop control systems with nonlinear dynamics over fully homomorphic encryption (FHE). Unlike differential privacy and output masking, FHE is a cryptographic primitive that provides assumption-based confidentiality guarantees under standard hardness assumptions. We observe that existing encrypted control frameworks remain largely limited to linear open-loop systems, primarily due to two key challenges: rapid ciphertext noise accumulation in feedback loops and the substantial computational overhead of nonlinear operations. In control systems, feedback is essential for real-time error correction, while nonlinear characteristics are critical for accurately modelling complex system behaviours. To address these challenges, we propose ENClose, a novel encrypted control framework that enables low-latency execution of both feedback control and nonlinear function evaluation. Specifically, ENClose introduces a low-latency homomorphic nonlinear computation framework that accelerates functional bootstrapping (FBS) by combining function segmentation with tree-based encrypted selection. This framework not only mitigates noise accumulation in encrypted feedback loops but also significantly improves the efficiency of FBS under high-precision settings, meeting the computational demands of dynamic control systems. Experimental results show that ENClose achieves a 3× to 20× speedup over state-of-the-art encrypted controllers. We validate ENClose through real-world applications, including multi-vehicle formation, spring–mass–damper control, and anomaly recovery, where the results demonstrate high-precision tracking and successful reconvergence after anomalies.