Secure Encoding Scheme for Consensus of Second-order Multi-Agent Systems

We consider the problem of consensus of a second-order multi-agent system in the situation where an eavesdropper tends to impact the security of the network. A secure encoding scheme that guarantees both consensus and security of the multi-agent network is designed. In the network, the agents transmit messages to one another through digital channels, and there exists an eavesdropper whose aim is to overhear the state information of the agents in the network. Instead of transmitting the states of themselves, the agents in the network send states of auxiliary systems to defend against the eavesdropper. The concept of topological entropy is utilized to restrict the eigenvalues of the encoding matrix. A sufficient condition is given to guarantee that the network achieves consensus, and the eavesdropper cannot get the accurate estimation of the state of any agent. A simulation example is given to show the performance of the agents and the eavesdropper under the designed encoding scheme.