Privacy preserving prescribed-time consensus in second-order nonlinear multi-agent systems

Abstract

In cooperative systems, information exchange is essential for achieving consensus, and the preservation of data privacy has attracted growing attention. However, most existing studies have been limited to first-order multi-agent systems. This study investigates the privacy-preserving consensus problem of second-order agents with Lipschitz-type nonlinearities. A novel masking scheme based on specific power functions is proposed to conceal the true states of the agents, which differs significantly from existing obfuscation methods. Meanwhile, by integrating a high-gain prescribed-time controller, second-order consensus is achieved within a user-defined time frame. As a consequence, the agents’ initial true states, including positions and velocities, are effectively safeguarded. A sufficient condition is derived for determining the control parameters, thereby elucidating the influence of agent dynamics, network topology, and control parameters. Additionally, despite the presence of high-gain and masking signals, the resulting controllers are proven to be bounded. Finally, several numerical examples are provided to validate the theoretical findings and demonstrate the effectiveness of the proposed control strategies.