Encrypted Decentralized Multi-Agent Optimization for Privacy Preservation in Cyber-Physical Systems

Decentralized optimizations have been extensively applied in large-scale industrial cyber-physical systems to achieve control scalability. However, state-of-the-art methods heavily depend on explicit communications between participants, exposing the entire control framework to data confidentiality risks. To overcome this challenge, in this article, a privacy-preserving decentralized multi-agent cooperative optimization paradigm was developed via integrating cryptography into decentralized optimization. The proposed approach can effectively protect participants' privacy against external eavesdroppers, honest-but-curious agents, and the system operator. Theoretical security and correctness analyses are provided. Simulations of numerical examples and experiments on a real-world platform are given to demonstrate the security, accuracy, and applicability of the proposed method.