Unified understanding and new results of controllability model of multi‐agent systems. (12th April 2022)

• Record Type: Journal Article
• Authors: Guo, Junhao; Ji, Zhijian; Liu, Yungang; Lin, Chong
• Is Part Of: International journal of robust and nonlinear control. Volume 32:Number 11(2022)
• Page Start: 6330
• Page End: 6345
• Publication Date: 2022-04-12
• Subjects: controllability -- equivalent partition -- multi‐agent systems -- UI$$ {U}_I $$ control; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.6140
• Languages: English
• ISSNs: 1049-8923

Abstract

Abstract: In this article, the effects of different models on the controllability of leader‐follower dynamics system based on Laplacian matrix are studied, and the controllability results applicable to general model are obtained. Our research is based on three different control modes, namely, broadcast control, U I $$ {U}_I $$ control, and non‐broadcast control, which cover all the control modes in the general model. Specifically, we first identify the relation of different U I $$ {U}_I $$ control, that is, if the system is controllable under i 1 $$ {i}_1 $$ different control signals, then increasing the number of control signals does not change the controllability of the system. Furthermore, it is proved that in a fixed topology, when the number of control inputs is increased, the controllability of the system is not correlated with the controllability of the original system, which appears counter‐intuitive. But the spectral radius of the Gramian matrix of the controllable system is increased. In addition, we analyze the condition number of Gramian matrix. Based on the above conclusions, we put forward the concept of hierarchical equivalent partition (HEP), and prove that under the general model, the existence of HEP makes the system uncontrollable. Finally, we expect to find a way to make the system controllable under the general model. Therefore, we obtain sufficient conditions for the system to be controllable. As a by‐product, we find that there is no completely uncontrollable graph when the general model with broadcast control is removed.