Controllability of a Leader–Follower Dynamic Network With Switching Topology

Liu, Bo; Chu, Tianguang; Wang, Long; Xie, Guangming

doi:10.1109/tac.2008.919548

Cited by 280 publications

(172 citation statements)

References 31 publications

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“…In the second case, the same leader set S is chosen and used for all topologies [84]. Under this strategy, we consider two possible leader selection metrics, namely the average-case…”

Section: Leader Selection Under Switching Between Predefined Topologiesmentioning

confidence: 99%

“…Leaders can be selected in order to improve robustness to these noise injection attacks in two ways. In the first case, a fixed set of leaders is used for the lifetime of the system, and hence must be chosen to minimize the worst-case error [84]. In the second case, the nodes may be equipped with sensing hardware that allows them to monitor their environment, observe increased noise levels, and update the set of leaders accordingly [89].…”

Section: Robustness To Link Noise Injection Attacksmentioning

confidence: 99%

“…Moreover, in [84,129], the authors showed that the follower node states are controllable from a set of leader nodes if the eigenvalues of the graph Laplacian are distinct. While these existing results imply that the follower node states can be driven to any value asymptotically, the convergence requires an arbitrary length of time, and the follower nodes' intermediate states prior to convergence may deviate significantly from their desired steady-state values.…”

Section: Smooth Convergencementioning

confidence: 99%

“…While some necessary and sufficient conditions for controllability of switched systems are in the existing literature [84], currently there is no efficient algorithm for selecting leaders to guarantee controllability under dynamic network topologies, let alone joint performance and controllability. State-dependent networks, in which the network topology is determined by the node states (e.g., the node positions), which are in turn affected by the choice of control inputs, represent another class of networked systems for which guaranteeing controllability is an open problem.…”

Section: Future Workmentioning

confidence: 99%

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Submodularity in Dynamics and Control of Networked Systems

Clark

Alomair

Bushnell

et al. 2016

Communications and Control Engineering

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Submodularity in Dynamics and Control of Networked Systems Andrew ClarkCo-Chairs of the Supervisory Committee:Radha Poovendran Electrical Engineering Linda Bushnell Electrical EngineeringControlling a networked dynamical system to reach a desired state is a fundamental challenge in applications including transportation, energy, social, and biological systems. One scalable approach to controlling such systems is to directly control the states of a subset of leader nodes, while relying on local interactions to steer the remaining nodes towards their desired states. The choice of leader nodes is known to affect system metrics including robustness to noise, rate of convergence to a desired state, and controllability of the system.Selecting an optimal subset of leader nodes, however, is inherently a combinatorial problem, making optimal leader node selection intractable in general.This thesis presents a submodular optimization framework to selecting leader nodes for control of networked systems. We investigate the problem of selecting a subset of leader nodes in order to minimize node state errors due to noise in the communication links between nodes. We prove that the error due to link noise is a supermodular function of the set of leader nodes, leading to the first polynomial-time algorithms for minimizing error due to link noise with provable optimality bounds. We develop our approach for networks with static topologies, as well as dynamic topologies due to random link failures, switching between predefined topologies, and arbitrary mobility.We study selecting leader nodes in order to minimize convergence error, defined as the error in the intermediate node states prior to reaching their desired values. We derive upper bounds for a class of convergence error metrics based on the hitting time of random walk on the network, which we prove to be a supermodular function of the set of input nodes.We present polynomial-time algorithms for minimizing convergence error with provable optimality bounds, for static as well as dynamic networks.Efficient algorithms have recently been proposed for selecting leader nodes to satisfy controllability, defined as the ability to drive the non-input nodes from any initial state to any desired state in finite time. These algorithms, however, do not incorporate performance criteria including robustness to noise and convergence rate. We study the problem of leader selection for joint performance and controllability, and prove that controllability can be formulated as a matroid constraint on the set of leader nodes. We propose efficient algorithms with provable optimality gap for selecting leader nodes for joint performance and controllability, and characterize the submodular structure of the largest controllable subgraph of a network.We also investigate selecting input nodes for guaranteeing synchronization in networked systems. Using the widely-studied Kuramoto model of nonlinear phase-coupled oscillators, we develop novel threshold-based conditions for a set of input nodes to ...

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“…In the second case, the same leader set S is chosen and used for all topologies [84]. Under this strategy, we consider two possible leader selection metrics, namely the average-case…”

Section: Leader Selection Under Switching Between Predefined Topologiesmentioning

confidence: 99%

Section: Robustness To Link Noise Injection Attacksmentioning

confidence: 99%

Section: Smooth Convergencementioning

confidence: 99%

Section: Future Workmentioning

confidence: 99%

See 2 more Smart Citations

Submodularity in Dynamics and Control of Networked Systems

Clark

Alomair

Bushnell

et al. 2016

Communications and Control Engineering

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show abstract

“…In [7], the controllability was characterized by graph theory. In [12], the controllability problem was studied under both fixed and switching topologies for continuous-time case, and then for discrete-time case [11]. Different from the classical control system, the dynamical behavior of networked systems heavily relies on how the network is connected, i.e.…”

Section: Introductionmentioning

confidence: 99%

Interconnection topologies for multi-agent coordination under leader–follower framework

et al. 2009

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In this paper, the formation control of networks of multiple agents is studied via controllability, where the network is under leader-follower structure with some agents taking the leader role and others being followers interconnected via neighbor-based rule. It is shown that the controllability of a multi-agent system is uniquely determined by the topology structure of interconnection graph, and the investigation of which comes down to that for a multi-agent system with the interconnection graph being connected. Based on these observations, two kinds of interconnection graph topologies are characterized, under which the network of multiple agents is uncontrollable, revealing to some extent how the controllability, and accordingly the formation control, are affected by the interconnection topology between agents. Finally, a necessary and sufficient condition in terms of eigenvector is presented. The results also touch upon the selection of leaders and are illustrated by several examples.

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Digraphs with Distinguishable Dynamics Under the Multi‐Agent Agreement Protocol

Rahimian¹,

Ajorlou²,

Aghdam³

2014

Asian Journal of Control

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In this work the ability to distinguish digraphs from the output response of some observing agents in a multi-agent network under the agreement protocol has been studied. Given a fixed observation point, it is desired to find sufficient graphical conditions under which the failure of a set of edges in the network information flow digraph is distinguishable from another set. When the latter is empty, this corresponds to the detectability of the former link set given the response of the observing agent. In developing the results, a powerful extension of the all-minors matrix tree theorem in algebraic graph theory is proved which relates the minors of the transformed Laplacian of a directed graph to the number and length of the shortest paths between its vertices. The results reveal an intricate relationship between the ability to distinguish the responses of a healthy and a faulty multi-agent network and the inter-nodal paths in their information flow digraphs. The results have direct implications for the operation and design of multi-agent systems subject to multiple link losses. Simulations and examples are presented to illustrate the analytic findings.

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Controllability of a Leader–Follower Dynamic Network With Switching Topology

Cited by 280 publications

References 31 publications

Submodularity in Dynamics and Control of Networked Systems

Submodularity in Dynamics and Control of Networked Systems

Interconnection topologies for multi-agent coordination under leader–follower framework

Digraphs with Distinguishable Dynamics Under the Multi‐Agent Agreement Protocol

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