Regular Papers

International Journal of Control, Automation and Systems 2014; 12(2): 231-240

Published online May 11, 2017

https://doi.org/10.1007/s12555-013-0220-8

© The International Journal of Control, Automation, and Systems

Consensus in Multi-Agent Systems with Nonlinear Uncertainties under a Fixed Undirected Graph

Jie Luo* and Chengyu Cao

The University of Connecticut

Abstract

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 L1 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.

Keywords Adaptive control, consensus, multi-agent system, nonlinear uncertainties.

Article

Regular Papers

International Journal of Control, Automation and Systems 2014; 12(2): 231-240

Published online April 1, 2014 https://doi.org/10.1007/s12555-013-0220-8

Copyright © The International Journal of Control, Automation, and Systems.

Consensus in Multi-Agent Systems with Nonlinear Uncertainties under a Fixed Undirected Graph

Jie Luo* and Chengyu Cao

The University of Connecticut

Abstract

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 L1 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.

Keywords: Adaptive control, consensus, multi-agent system, nonlinear uncertainties.

IJCAS
May 2024

Vol. 22, No. 5, pp. 1461~1759

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