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 realworld applications, including multi-vehicle formation, spring–mass–damper control, and anomaly recovery, where the results demonstrate high-precision tracking and successful reconvergence after anomalies.

We propose an encrypted controller framework for linear time-invariant systems with actuator non-linearity based on fully homomorphic encryption (FHE). While some existing works explore the use of partially homomorphic encryption (PHE) in implementing linear controller systems, the impacts of the non-linear behaviors of the actuators on the systems are often left unconcerned. In particular, when the inputs to the controller become too small or too large, actuators may burn out due to unstable system state oscillations. To solve this dilemma, we design and implement FHECAP, an FHEbased controller framework that can homomorphically apply non-linear functions to the actuators to rectify the system inputs. In FHECAP, we first design a novel data encoding scheme tailored for efficient gain matrix evaluation. Then, we propose a high-precision homomorphic algorithm to apply non-arithmetic piecewise function to realize the actuator normalization. In the experiments, compared with the existing state-of-the-art encrypted controllers, FHECAP achieves 4×–1000× reduction in computational latency. We evaluate the effectiveness of FHECAP in the real-world application of encrypted control for spacecraft rendezvous. The simulation results show that the FHECAP achieves real-time spacecraft rendezvous with negligible accuracy loss.