Flocking for multi-agent systems with unknown nonlinear time-varying uncertainties under a fixed undirected graph

Abstract

This paper presents a flocking algorithm for networked multi-agent systems with unknown, nonlinear, time-varying uncertainties by integrating cooperative control and ${\mathcal{L}}_1$ adaptive control methods. 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 flocking under a fixed and connected undirected graph. Information of ideal states, instead of real states, is exchanged among agents through a communication network. The presence of uncertainties will lead to the degeneration of the performance or even destabilize the entire multi-agent system. The ${\mathcal{L}}_1$ adaptive control law is therefore introduced to handle unknown, nonlinear, time-varying uncertainties. By integrating the cooperative control law with the adaptive control law, the real multi-agent system stays close to the ideal multi-agent system which achieves flocking asymptotically under a connected graph. Simulation results of two-dimensional flocking with uncertainties are provided to demonstrate the presented flocking algorithm.

Keywords:

• adaptive control
• cooperative control
• flocking
• multi-agent system

Additional information

Funding

This work is supported by NSF [grant number IIS–1208499]; NASA [grant number FRS# 5617760].