Encrypted explicit MPC based on two-party computation and convex controller decomposition

Abstract

Encrypted control enables confidential controller evaluations in cloud-based or networked control systems. From a technical point of view, an encrypted controller is a modified control algorithm that is capable of computing encrypted control actions based on encrypted system states (without decrypting the states). A key technology for the design of encrypted controllers is homomorphic encryption that allows simple mathematical operations to be carried out on encrypted data. As apparent from existing schemes, one of the main challenges in encrypted control is to reformulate given control laws such that they can be merged with these special cryptosystems.In this paper, a novel encrypted implementation of model predictive control (MPC) is presented. We utilize that MPC for linear systems with polytopic constraints is well known to result in a continuous piecewise affine (PWA) control law. Thus, we can apply techniques for the decomposition of PWA functions into two convex PWA parts. The convexity of the decomposed parts finally allows us to realize a secure two-party evaluation of the original PWA function and, hence, of explicit MPC. Compared to existing encrypted MPC schemes, the novel approach makes significantly better use of computational resources offered by the two involved clouds.