Data-driven adaptive consensus for linear multi-agent systems: A scalable distributed protocol

Abstract

This paper is concerned with the noiseless and noisy data-driven consensus problem of general linear multi-agent systems (MASs) with unknown agent dynamics. First, a data-driven adaptive scheme is designed to enable each edge to tune its weight in an on-line fashion. Subsequently, a distributed noiseless data-driven adaptive consensus (DDAC) protocol is established for the MASs so as to ensure guaranteed consensus. In this protocol, agents communicate with their neighbors through an undirected and connected graph. Importantly, this protocol is proven to be independent of both system model knowledge and be scalable with respect to the size of communication network. Moreover, to address the scenario of a directed communication graph, a modified node-based adaptive scheme, which relies solely on data, is introduced, along with a refined DDAC protocol. The conditions for achieving consensus are derived as semi-definite programs, and the corresponding feasibility is analyzed. Furthermore, the paper considers a noisy data scenario and tackles the consensus problem with a noisy data by employing a refined adaptive scheme and establishing a distributed noisy DDAC protocol. Compared to existing consensus protocols, our DDAC protocol offers high flexibility and scalability by eliminating the need for a system model and global network information. Finally, three examples are provided to verify the effectiveness of the proposed DDAC protocols.