# Symmetries and isomorphisms for privacy in control over the cloud

## TL;DR

This paper introduces transformation-based methods to enhance data privacy in cloud-controlled feedback systems, analyzing privacy guarantees across different levels of adversary knowledge with minimal impact on control performance.

## Contribution

It proposes novel privacy-preserving transformations tailored for cloud control, quantifies privacy levels, and examines privacy loss with side knowledge in various scenarios.

## Key findings

- Methods effectively protect private data during cloud control.
- Quantitative analysis of privacy leakage with side knowledge.
- Control performance remains minimally affected.

## Abstract

Cloud computing platforms are being increasingly used for closing feedback control loops, especially when computationally expensive algorithms, such as model-predictive control, are used to optimize performance. Outsourcing of control algorithms entails an exchange of data between the control system and the cloud, and, naturally, raises concerns about the privacy of the control system's data (e.g., state trajectory, control objective). Moreover, any attempt at enforcing privacy needs to add minimal computational overhead to avoid degrading control performance. In this paper, we propose several transformation-based methods for enforcing data privacy. We also quantify the amount of provided privacy and discuss how much privacy is lost when the adversary has access to side knowledge. We address three different scenarios: a) the cloud has no knowledge about the system being controlled; b) the cloud knows what sensors and actuators the system employs but not the system dynamics; c) the cloud knows the system dynamics, its sensors, and actuators. In all of these three scenarios, the proposed methods allow for the control over the cloud without compromising private information (which information is considered private depends on the considered scenario).