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

This paper 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. Firstly, 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. Secondly, a privacy attack model is developed in this paper, 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 can not 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.