Homomorphically Encrypted Robust MPC for Privacy-Preserving Control Under System Uncertainties

In this paper, a homomorphically encrypted robust model predictive control (HERMPC) is proposed to address privacy and security concerns in the cloud-based control of polytopic uncertain systems. Firstly, an RMPC framework that incorporates semi-homomorphic encryption is developed for the secure control of uncertain systems. Secondly, an RMPC optimization problem is formulated, in which both control gain quantization errors and model parameter uncertainties are explicitly taken into account. The concept of quadratic boundedness is employed to handle deviations caused by the quantization of measured states. Thirdly, a HERMPC algorithm is proposed, and conditions are derived for the quantization and encryption parameters to guarantee bounded control performance and stability. Finally, the effectiveness of the proposed method is validated through a numerical example, demonstrating its capability to ensure system stability while preserving privacy and security.