Privacy-Protected and Prescribed-Time Dynamic Average Consensus Over Directed Networks: An Integral Surplus-Based Approach

This article addresses the design problem of the privacy-protected and prescribed-time dynamic average consensus (DAC) algorithm over possibly unbalanced directed networks—the most general and most challenging case from the perspective of typologies, which has been rarely studied in existing literature. First, by developing an integral surplus-based prescribed-time control framework, a prescribed-time DAC algorithm is designed over unbalanced directed networks, which allows all agents to achieve DAC with minimal steady-state error in a prescribed-settling time. Compared with existing works on DAC, it is the first time to solve the prescribed-time problem over directed networks. Second, a privacy attack model is developed in this article, which may help an external eavesdropper easily wiretap the privacy-sensitive data in the existing DAC algorithms. To avoid the privacy data leakage, a state decomposition scheme is embedded in the proposed prescribed-time DAC algorithm with privacy-protected requirements. With the help of privacy-protected DAC algorithms, the previous privacy attack model cannot wiretap the privacy-sensitive data of agents anymore. Finally, some simulation examples display the validity of the proposed privacy-protected and prescribed-time DAC algorithms.