PI Observer-Based Consensus of Nonlinear Multi-Agent Systems Via Reduced-Order Edge-State Dynamics and Decentralized Procedure

This paper proposes a novel framework for studying the consensus problem for a class of nonlinear multi-agent systems (MASs) based on decentralized output- feedback stabilization of derived reduced-order fundamental edge-state dynamic systems. Firstly, by introducing edge-state dynamics with respect to a directed spanning tree (DST) of the communication topology, we equivalently transform the state consensus problem into a decentralized output feedback stabilization problem. Then, for the case of linear MASs, we derive a new sufficient and necessary consensus criterion in terms of the concept of decentralized fixed modes (DFMs) and also present a design procedure of the protocol gains in terms of linear matrix inequalities (LMIs). Next, a sufficient consensus condition is derived in terms of LMIs for the nonlinear MAS with local proportional- integral (PI) observers. Furthermore, to reduce the complexity of the condition verification, we introduce a graph representation of the fundamental edge-state dynamic system and decompose it into strongly connected components, and thus reorganize the condition in a decentralized form. On this basis, we present a hierarchical method to design the consensus protocols and PI observers based on the information of the subsystems itself only. Finally, several numerical examples are given to illustrate the effectiveness of the proposed method.