Fully Distributed Minimal-order Attack-free Protocol for Nonlinear Multi-agent Networks

Achieving fully distributed consensus in multi-agent networks (MANs) based on relative output information is of significant importance in the field of distributed cooperative control. Despite the recent development of consensus theory, there is still lack of an efficient approach to constructing fully distributed consensus protocols for MANs using only relative output measurements, especially for the case with inherent nonlinear agent dynamics under directed communication graphs. This paper studies fully distributed minimal-order protocol design for consensus of MANs with Lipschitz-type nonlinear agent dynamics under general directed communication graphs. It is revealed that the minimal order of the observer estimating consensus error equals the difference between the dimension of a single agent's state vector and the rank of the output matrix of the agent. Based on the designed distributed minimal-order observer, fully distributed consensus protocols are developed. The proposed protocols have the abilities of reducing communication burden and also can avoid network attacks on the internal states. Numerical simulations are presented to illustrate the analytical results.