Cloud-based coordination of multi-agent systems requires sharing state with a central server, creating a conflict between coordination and privacy. Fully homomorphic encryption (FHE) resolves this in principle, but its severe arithmetic constraints demand that every stage of the control loop be redesigned from first principles. We present an end-to-end encrypted control pipeline in which sensing, state estimation, state propagation, and consensus control all operate on CKKS-encrypted data using only addition, multiplication, and cyclic rotation. In order to overcome the computational challenges of FHE, we employ steady-state Kalman gains instead of solving for the matrices online and graph Laplacians are applied via the diagonal method at a cost proportional to the number of nonzero cyclic diagonals, accommodating ring, torus, and complete-graph topologies within a unified framework. To quantify the cumulative effect of encryption noise, we use the separation principle to decouple controller and observer error dynamics and derive a periodic bootstrapping bound in which CKKS bootstrapping acts as an impulsive disturbance; the resulting steady-state error ball depends on the bootstrapping precision and the closed-loop spectral radius, providing a direct design equation for the privacy-accuracy tradeoff. The pipeline is validated on a multi-agent formation control scenario, confirming stable closed-loop operation under encryption with bounded tracking error.

翻译：基于云端的多智能体系统协同需要将状态信息共享至中央服务器，这造成了协同性与隐私性之间的矛盾。全同态加密（FHE）在理论上可解决此问题，但其严格的算术约束要求控制回路中的每个阶段均需从基本原理层面重新设计。我们提出了一种端到端加密控制管道，其中感知、状态估计、状态传播和一致性控制均仅通过加法、乘法与循环移位操作对CKKS加密数据执行运算。为克服FHE的计算挑战，我们采用稳态卡尔曼增益替代在线求解矩阵，并通过对角化方法以非零循环对角矩阵数量成比例的计算代价施加图拉普拉斯算子，可在统一框架内兼容环形、环形面与完全图拓扑结构。为量化加密噪声的累积效应，我们利用分离定理解耦控制器与观测器误差动态，导出了周期性自举约束条件——其中CKKS自举过程表现为脉冲扰动；所得稳态误差球半径取决于自举精度与闭环谱半径，为隐私-精度权衡提供了直接的设计方程。该管道在多智能体编队控制场景中通过验证，证实了加密条件下具有有界跟踪误差的稳定闭环运行能力。