Unified understanding and new results of controllability model of multi‐agent systems

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 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 control, that is, if the system is controllable under 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.

An internal‐model‐based event‐triggered strategy for rendezvous with connectivity preservation problem of multi‐agent systems

“…Motivated by the wide applications in the military and engineering, during the last two decades, the control design for the multi‐agent systems have attracted a lot of attention, especially for those modeled by linear and nonlinear systems 1,2 . In order to implement the control law in the digital platform, the event‐triggered control design has been widely investigated in different scenarios, especially the consensus problem (see survey paper 3 ).…”

“…Motivated by the wide applications in the military and engineering, during the last two decades, the control design for the multi-agent systems have attracted a lot of attention, especially for those modeled by linear and nonlinear systems. 1,2 In order to implement the control law in the digital platform, the event-triggered control design has been widely investigated in different scenarios, especially the consensus problem (see survey paper 3 ). Compared with periodic and frequent samplings, it is advantageous to avoid redundant data transmissions and thus can utilize the limited control task execution capability more efficiently and save energy resources in the digital platform.…”