Towards privacy-preserving cooperative control via encrypted distributed optimization

TL;DR

This work addresses the privacy risks inherent in distributed cooperative control by proposing a privacy-preserving scheme based on encrypted distributed optimization. The authors develop an encrypted ADMM framework that preserves neighbor privacy through homomorphic encryption and key-switching across multiple ciphertext instances, enabling secure distributed optimization for a general consensus problem. They explicitly model the privacy constraints on local and neighbor quantities, and provide security guarantees under an honest-but-curious attacker model, including detailed protocol and key-management considerations. A robot-formation case study demonstrates that encrypted ADMM can closely match centralized performance while highlighting real-time computational challenges and potential for future hardware-accelerated or alternative cryptographic approaches. Overall, the work offers a principled, scalable method for privacy-preserving coordination in multi-agent systems with practical implications for cyber-physical security and autonomous collaboration.

Abstract

Cooperative control is crucial for the effective operation of dynamical multi-agent systems. Especially for distributed control schemes, it is essential to exchange data between the agents. This becomes a privacy threat if the data is sensitive. Encrypted control has shown the potential to address this risk and ensure confidentiality. However, existing approaches mainly focus on cloud-based control and distributed schemes are restrictive. In this paper, we present a novel privacy-preserving cooperative control scheme based on encrypted distributed optimization. More precisely, we focus on a secure distributed solution of a general consensus problem, which has manifold applications in cooperative control, by means of the alternating direction method of multipliers (ADMM). As a unique feature of our approach, we explicitly take into account the common situation that local decision variables contain copies of quantities associated with neighboring agents and ensure the neighbor's privacy. We show the effectiveness of our method based on a numerical case study dealing with the formation of mobile robots.

Figures (2)

• Figure 1: Exemplary communication graphs. The first two graphs offer specific structures, while the latter is generic.
• Figure 2: Experimental results for the graphs from Fig. \ref{['fig:threeGraphs']}. The centralized, distributed, and encrypted solution are depicted in green, red, and blue, respectively. Solid lines represent the robot's trajectories, with circles marking the initial position. Crosses mark the ideal position and dashed lines (in green, red, and blue) show the actual formation at $t=20$.