Structural controllability of high order dynamic multi-agent systems

Abstract

Recently, the controllability problem of multi-agent systems is significantly explored; however, the majority of studies have been focused on the classical controllability approaches. This paper investigates the necessary and sufficient conditions of structural controllability for high order dynamic multi-agent systems. We consider a group of agents in a leader-follower framework under a fixed topology structure. It is assumed that, the agents interconnection is a weighted graph with freely chosen weights and each agent has a high order controllable canonical dynamic. Under this setup we show that the structural controllability of such a network is directly determined by agent interconnection. It is shown that a set of weights can be found which make the entire network controllable if and only if the graph is connected. Finally, we present a numerical example and simulation to illustrate the results.

On the controllability and weight controllability of double integrator consensus systems

“…Therefore, somewhat surprisingly, in this case our necessary and sufficient condition for weight controllability is the same condition that [7] obtain for structural controllability. While it is clear from the problem setup that LF connectedness will be necessary for any kind of LF controllability, we would not expect it to be sufficient as well, even in this simplified case.…”

“…It is thus a natural extension of the problem to study whether the LFCS (3) can be made controllable by allowing the communication links to have different weights. In [7] this question has been linked with the notion of structural controllability of the matrix pair 0 I Ax Aẋ , ( 0 B ) , that is obtained by rewriting (3) as a single integrator system. However this existing work suffers from one major drawback.…”

“…Furthermore, the identitiy matrix in the formulation of [7] indicates integration of the state variable and has to be assumed as fixed. Thus, though the system might be structurally controllable in the case that all entries of the system matrices are "free", it is yet to be shown that it is controllable without destroying the particular consensus structure of the system.…”

Studies on strong structural controllability and optimum link weight assignment of complex networks

“…Such kinds of agent based complex networks hail from domains like cooperative control of unmanned aerial vehicles, smart grid, infrastructure less networks like wireless sensor networks (WSN), self-organizing networks, swarm robot coverage and locomotion control and many others [1]- [9]. These application domains can always be described with the key term, namely "Multi-Agent System" [3], [5], [11], [13], [14].…”

“…In [11], the authors considered the system as a single integrator dynamic agent. Based on this work, double integrator [15] and high order integrator [13], [15] were taken into account. First, the structural controllability problem was proposed from graph theoretic point of view for multi-agent system in [11], and [12].…”