Secure Formation Control via Edge Computing Enabled by Fully Homomorphic Encryption and Mixed Uniform-Logarithmic Quantization

TL;DR

This paper proposes a secure distributed formation control system using edge computing, fully homomorphic encryption, and a novel mixed uniform-logarithmic quantizer to ensure privacy and stability in real-time networked control.

Contribution

It introduces a new quantization method compatible with FHE-LWE for secure control, along with stability analysis of the secure formation control system.

Findings

The proposed MULQ effectively quantizes real-time data within bounded plaintext space.

The secure control system maintains asymptotic stability.

Simulation results validate the effectiveness of the proposed approach.

Abstract

Recent developments in communication technologies, such as 5G, together with innovative computing paradigms, such as edge computing, provide further possibilities for the implementation of real-time networked control systems. However, privacy and cyber-security concerns arise when sharing private data between sensors, agents and a third-party computing facility. In this paper, a secure version of the distributed formation control is presented, analyzed and simulated, where gradient-based formation control law is implemented in the edge, with sensor and actuator information being secured by fully homomorphic encryption method based on learning with error (FHE-LWE) combined with a proposed mixed uniform-logarithmic quantizer (MULQ). The novel quantizer is shown to be suitable for realizing secure control systems with FHE-LWE where the critical real-time information can be quantized into a prescribed bounded space of plaintext while satisfying a sector bound condition whose lower and upper-bound can be made sufficiently close to an identity. An absolute stability analysis is presented, that shows the asymptotic stability of the closed-loop secure control system.