Consensus in multi-agent systems with nonlinear uncertainties under a fixed undirected graph

This paper presents consensus algorithms by integrating cooperative control and adaptive control laws for multi-agent systems with unknown nonlinear uncertainties. An ideal multi-agent system without uncertainties is introduced first. The cooperative control law, based on an artificial potential function, is designed to make the ideal multi-agent system achieve consensus under a fixed and connected undirected graph. The presence of uncertainties will degenerate the performance, or even destabilize the whole multi-agent system. The L ₁ adaptive control law is therefore introduced to handle unknown nonlinear uncertainties. Two different consensus cases are considered: 1) normal consensus—where all agents reach an agreement on an initially undetermined position and velocity, and 2) consensus with a virtual leader—where all agents’ states converge to the virtual leader’s states. Under a fixed and connected undirected graph, the presented consensus algorithms enable the real multi-agent system to stay close to the ideal multi-agent system which achieves consensus with or without a virtual leader. Simulation results of 2-D consensus with nonlinear uncertainties are provided to demonstrate the presented algorithms.