Controllability of multi-agent systems based on agreement protocols

Abstract

This paper investigates the controllability of multi-agent systems based on agreement protocols. First, for a group of single-integrator agents, the controllability is studied in a unified framework for both networks with leader-following structure and networks with undirected graph. Some new necessary/sufficient conditions for the controllability of networks of single-integrator agents are established. Second, we prove that, under the same topology and same prescribed leaders, a network of high-order dynamic agents is completely controllable if and only if so is a network of single-integrator agents. Third, how the selection of leaders and the coupling weights of graphs affect the controllability is analyzed. Finally, some numerical simulations are presented to demonstrate the effectiveness of the theoretical results.

Structural controllability of high order dynamic multi-agent systems

“…In [16] it is considered the position and velocity states of agents and investigated the controllability of double order integrator dynamic systems. [17] extended this work for high order integrator models. They achieved interesting results which imply that the controllability of a network constructed by high ordered integrator agents has the same properties as networks based on single-integrator agents under the same interconnection and same leaders position.…”

Controllability of discrete-time multi-agent systems with directed topology and input delay

“…In Wang et al (2009), the controllability of first-order, high-order continuous-time multi-agent system is equivalent to that of (L ff , L fl ). However, the controllability of second-order discrete-time multi-agent system is equivalent to that of (L ff , L fl ) if protocols include relative velocities and positions as well as feedback gains p, k 1 and sampling period T satisfy some conditions.…”

“…Email: longwang@pku.edu.cn is equivalent to that of a pair of submatrices of Laplacian matrix. In what follows, some related results on the controllability of continuous-time systems are proposed, such as first-order and high-order multi-agent systems in Wang, Jiang, Xie, and Ji (2009), switching topology and time delay in Ji, Wang, Lin, and Wang (2010), equitable and relaxed equitable partition in Rahmani, Ji, Mesbahi, and Egerstedt (2009) and external equitable partition in O'Clery, Yuan, Stan, and Barahona (2013). For the controllability of discrete-time systems, the controllability conditions for first-order multi-agent systems with switching topology are proposed in Liu, Chu, Wang, and Xie (2008).…”

“…Previous research has elucidated that the neighbour-based protocol plays a vital role in the investigation. With two agreement protocols, Wang et al (2009) have shown that the controllability of high-order multi-agent systems is equivalent to that of a pair of submatrices of Laplacian matrix. In case of general linear multi-agent systems, Ji et al (2014) have proposed a neighbour-based protocol and revealed that the controllability can be guaranteed by that of a pair of 2 Z.…”

Controllability Synthesis of Compartmental Networks with Single Leader

“…Liu et al [19] addressed the controllability of discrete-time multi-agent systems with switching network topologies. Wang et al [20] discussed the influence on controllability by different leader assignments and communication links. Ji et al [21] proposed conditions for network controllability, which are analogous to the early results in [5].…”