Event-trigger Optimal Consensus for Multi-agent System Subject to Differential Privacy

Optimal consensus algorithm is a very useful consensus algorithm for distributed cooperative control, which makes all the agents not only achieve consensus but also minimize the cost function. However, to achieve consensus, agents need to exchange their state with each other on public channel. If attackers want to obtain the privacy information of agents, they only need to monitor the public channel. To solve this problem, a novel event-triggered differentially privacy optimal consensus algorithm is proposed to preserve the privacy of the cost function of each agent in the whole process of consensus computation. Based on event-trigger condition, we analyze the consensus of our algorithm in detail, including the accuracy and consensus conditions. In addition, the privacy-preserving analysis are also given, which exhibits that privacy of the states of all agents can be preserved. The privacy level and the sensitivity of the differential privacy are also obtained. Finally, a numerical simulation is given to illustrate the effectiveness of the theoretical results.