Distributed dynamic average consensus for nonlinear multi-agent systems in the presence of external disturbances over a directed graph

Abstract

This paper investigates distributed dynamic average consensus problems for a class of nonlinear multi-agent systems in the presence of local disturbances over a directed graph, where local disturbances are generated by an external system. In order to solve such problems, we establish a distributed consensus protocol based on the internal model (IM) principle such that states of the first-order nonlinear system converge to the average of multiple time-varying inputs and local disturbances are rejected. By means of Lyapunov stability theory and graph theory, a two-step mechanism is established to certify that the proposed algorithm is exponentially convergent. Furthermore, a neoteric distributed consensus algorithm is proposed to solve a dynamic average consensus problem of the second-order nonlinear multi-agent system. The proposed algorithm can guarantee that positions and velocities of the second-order nonlinear multi-agent system converge exponentially to the average of multiple time-varying inputs and their derivative and local disturbances are rejected, respectively. Finally, three numerical examples are provided to demonstrate the effectiveness of the obtained results.