Interacting with Networks: How Does Structure Relate to Controllability in Single-Leader, Consensus Networks?

Abstract

As networked dynamical systems appear around us at an increasing rate, questions concerning how to manage and control such systems are becoming more important. Examples include multi-agent robotics, distributed sensor networks, interconnected manufacturing chains, and data networks. In response to this growth, a significant body of work has emerged focusing on how to organize such networks in order to facilitate their control and make them amenable to human interactions. In this article, we summarize these activities by connecting the network topology, that is, the layout of the interconnections in the network, to the classic notion of controllability.In manufacturing, one of the technological bottlenecks can be found in the general assembly phase. This is the last stage of the manufacturing chain where the pieces, such as doors, locks, and cup-holders in automotive manufacturing, are assembled into a finished product. If a single worker could command and interact with a number of flexible, mobile manipulators in an effective manner, it is expected that this process could be improved significantly. Similarly,

Graph partitions and cluster synchronization in networks of oscillators

“…The more general problem of obtaining all EEPs for a graph appears to be computationally more challenging 25,53 . However, there exist efficient algorithms to compute EEPs centered around a node 27,54 , which can be used to characterize the dynamical influence of particular nodes on the global dynamics of the network 26,27,29 .…”

Global Feedback Control for Coordinated Linear Switched Reluctance Machines Network with Full-State Observation and Internal Model Compensation

“…The gains of the controller and the observer can then be calculated, according to Equations (24) and (40). The gains are tabulated in Table 2.…”

“…A graph-theoretical characterization of controllability and observability for a leader-follower network is developed over the finite fields so that the quantized agents can be put into any desired configuration by a set of leader agents [23]. The relationship between the network topology and the controllability of the network containing a single leader is discussed, and some key results in this area are summarized [24]. The controllability and observability of a network with hybrid linear agents are investigated, and some necessary and sufficient conditions are derived from the Popov-Belevitch-Hautus (PBH) test [25].…”

Model reduction of linear multi-agent systems by clustering with $$\varvec{\mathcal {H}_2}$$ H 2 and $$\varvec{\mathcal {H}_\infty }$$ H ∞ error bounds

“…Widely studied topics in networked systems have been the problems of consensus and synchronization, see [19,20,27,30]. Other important subjects in the theory of networked systems are flocking, formation control, sensor placement, and controllability of networks, see, e.g., [8,9,11,12,24,29,34].…”