  Large-scale multi-agent cooperative control problems have materially enjoyed
the scalability, adaptivity, and flexibility of decentralized optimization.
However, due to the mandatory iterative communications between the agents and
the system operator, the decentralized architecture is vulnerable to malicious
attacks and privacy breach. Current research on addressing privacy preservation
of both agents and the system operator in cooperative decentralized
optimization with strongly coupled objective functions and constraints is still
primitive. To fill in the gaps, this paper proposes a novel privacy-preserving
decentralized optimization paradigm based on Paillier cryptosystem. The
proposed paradigm achieves ideal correctness and security, as well as resists
attacks from a range of adversaries. The efficacy and efficiency of the
proposed approach are verified via numerical simulations and a real-world
physical platform.
