Cloud-Based MPC with Encrypted Data

This paper explores the privacy of cloud out-sourced Model Predictive Control (MPC) for a linear system with input constraints. A client sends her private states to the cloud who performs the MPC computation and returns the control inputs. In order to guarantee that the cloud can perform this computation without obtaining anything about the client's private data, we employ a partially homomorphic cryptosystem. We propose protocols for two cloud-MPC architectures: a client-server architecture and a two-server architecture. In the first case, a control input for the system is privately computed by the cloud server with the assistance of the client. In the second case, the control input is privately computed by two independent, non-colluding servers, with no additional requirements from the client. We prove that the proposed protocols preserve the privacy of the client's data and of the resulting control input. Furthermore, we compute bounds on the errors introduced by encryption. We discuss the trade-off between communication, MPC performance and privacy.