On the Design of Optimal Consensus With Deception-Eliminating Scheme and Asynchronous Updates

This article investigates the deception-eliminating design (DED) against false information attacks by deceptive agents in asynchronous optimal consensus control. We model the asynchronous interactions among agents as multistage games and establish a Tit-for-Tat rule to compel deceptive agents to turn to transmitting true state information. Furthermore, we design a false information counterattack rule under asynchronous updates by leveraging the invariance of the rank of equivalent matrices and the convexity of positive semidefinite quadratic forms. This design effectively intimidates deceptive agents that have transitioned to cooperation, ensuring they do not revert to transmitting false information. Subsequently, by utilizing the properties of Riccati differential equations, the integrating factor methods, the Minkowski inequality, and proof by contradiction, we theoretically analyze the impact of false information on consensus and provide an explicit upper bound for the strategy update periods of agents with different performance matrices. Theoretical proof shows that as long as the strategy update periods of all agents remain below this upper bound and the above two DEDs are implemented, the asynchronous consensus is guaranteed.