Design of robust hierarchical control for homogeneous linear multi-agent systems with parametric uncertainty and external disturbance

Abstract

This paper presents the design of robust hierarchical control for homogeneous linear multi-agent systems (MAS) subject to parametric uncertainty and external disturbance. Specifically, the control design is based on a two-layer hierarchical structure consisting of an upper layer and a lower layer. In the lower layer, each agent is represented by a linear time-invariant system and executes a local action. Moreover, each agent exchanges information with neighbouring agents in the upper layer through an undirected graph to achieve the global goal of stabilisation and disturbance attenuation for the MAS. We propose two robust control designs, namely, robust ${\mathcal{H}}_{\mathrm{\infty }}$ hierarchical control and robust ${\mathcal{H}}_2$ hierarchical control. The design of local and global feedback control laws is formulated as a constrained optimisation over linear matrix inequalities (LMI). The LMI formulation can effectively incorporate the design objective to minimise disturbance attenuation. Numerical results show that the proposed robust controls ensure robust stability of MAS and outperform the existing nominal controls by improving the disturbance attenuation.

Keywords:

• Multi-agent systems (MAS)
• parametric uncertainty
• disturbance attenuation
• hierarchical control
• linear matrix inequality (LMI)
• $H_{\mathrm{\infty }}/H_2$

Acknowledgments

The first author thanked the International Institute for Carbon-Neutral Energy Research, Institute of Mathematics for Industry, Kyushu University for providing research facility during his research study.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Collaborative Research Grant from JICA Project for AUN/SEED-Net and the Research Grant from Rachadapisek Sompote Fund for Intelligent Control Automation of Process Systems Research Unit.