Privacy Preserving Prescribed-Time Consensus in Second-Order Nonlinear Multi-Agent Systems

Abstract

For cooperative systems, the information exchange is requisite for consensus reaching, and how to preserve the data privacy has received increasing attentions in many practical fields. Recognizing that most existing studies were confined in first-order multi-agent systems, this work investigates the privacy-preserving consensus of some second-order agents with Lipschitz nonlinearity, and proposes a novel masking policy in terms of certain power functions to conceal the agents' true states, differing from most existing obfuscation techniques. By incorporating a prescribed-time controller with high gain, second-order consensus is guaranteed in a certain user-defined time, and the agents' true initial states, i.e., the positions and velocities, are successfully protected. A sufficient criterion is established for deciding the control parameters, revealing the impact of the agent dynamics, topology, and control parameters. Meanwhile, the resultant controllers are also proved to be bounded in the spite of both high gain and masking signals. Some numerical examples are also given to demonstrate the validity of the theoretical results and the performance of the proposed control schemes.

Keywords: Privacy-preservation, prescribed-time consensus, second-order multi-agent system, high-gain control