Advances in Network Controllability

Xiang, Linying; Chen, Fei; Ren, Wei; Chen, Guanrong

doi:10.1109/mcas.2019.2909446

Cited by 112 publications

(64 citation statements)

References 96 publications

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“…In this regard, whether or not they can be controlled is essential, which leads to the fundamental concept of network controllability. Consequently, network controllability has become a focal issue in the studies of complex networks [5]- [15], where the concept of controllability refers to the ability of a network in moving from any of its initial state to any desired target state under an admissible control input within a finite duration of time. It was shown [5] that identifying the minimum number of external control inputs (recalled driver nodes) to achieve a full control of a directed network requires searching for a maximum matching of the network, which quantifies the network structural controllability.…”

Section: Introductionmentioning

confidence: 99%

Towards Optimal Robustness of Network Controllability: An Empirical Necessary Condition

Lou

Wang

Tsang

et al. 2020

IEEE Trans. Circuits Syst. I

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To better understand the correlation between network topological features and the robustness of network controllability in a general setting, this paper suggests a practical approach to searching for optimal network topologies with given numbers of nodes and edges. Since theoretical analysis is impossible at least in the present time, exhaustive search based on optimization techniques is employed, firstly for a group of small-sized networks that are realistically workable, where exhaustive means 1) all possible network structures with the given numbers of nodes and edges are computed and compared, and 2) all possible node-removal sequences are considered. An empirical necessary condition (ENC) is observed from the results of exhaustive search, which shrinks the search space to quickly find an optimal solution. ENC shows that the maximum and minimum in-and out-degrees of an optimal network structure should be almost identical, or within a very narrow range, i.e., the network should be extremely homogeneous. Edge rectification towards the satisfaction of the ENC is then designed and evaluated. Simulation results on large-sized synthetic and realworld networks verify the effectiveness of both the observed ENC and the edge rectification scheme. As more operations of edge rectification are performed, the network is getting closer to exactly satisfying the ENC, and consequently the robustness of the network controllability is enhanced towards optimum.

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Section: Introductionmentioning

confidence: 99%

Towards Optimal Robustness of Network Controllability: An Empirical Necessary Condition

Lou

Wang

Tsang

et al. 2020

IEEE Trans. Circuits Syst. I

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“…A global symmetry relationship was found, which accounts for the invariance of controllability with respect to exchanging the densities of any two different types of dynamic units, irrespective of the network topology. More general results on MIMO node systems can be found in [27], [28], [29] and the recent survey [30].…”

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confidence: 99%

Controllability of Directed Networked MIMO Systems With Heterogeneous Dynamics

Xiang

Wang

Chen

et al. 2020

IEEE Trans. Control Netw. Syst.

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This paper studies the controllability of networked multi-input-multi-output (MIMO) systems, in which the network topology is weighted and directed, and the nodes are heterogeneous higher-dimensional linear time-invariant (LTI) dynamical systems. The primary objective is to search for controllability criteria beyond those already known for homogeneous networks. The focus is on the effects of the network topology, node dynamics, external control inputs, as well as the inner interactions on the network controllability. It is found that a network of heterogeneous systems can be controllable even if the corresponding homogeneous network topology is uncontrollable. The finding thus unravels another fundamental property that affects the network controllability-the heterogeneity of the node dynamics. A necessary and sufficient condition is derived for the controllability of heterogeneous networked MIMO LTI systems. For some typical cases, necessary and/or sufficient controllability conditions are specified and presented on the node dynamics, inner interactions, as well as the network topology.

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“…Of particular interest here, is the extended definition of Zaidi [1], namely that it encapsulates the study of theory, methods and algorithms applicable to graph-based models representing interconnected real-world systems. From this perspective, the collection of interconnected elements of a finite element analysis of a distributed structure or physical field and a complex interconnection of nonlinear dynamical systems are instances of complex network analyses [2][3], the former undirected and the latter directed. Both an excellent account of the theory and overview of current research directions in complex networks, can be found in [4].…”

Section: Introductionmentioning

confidence: 99%

“…In the note, the term "system" refers to any object that can be satisfactorily approximated by some binary relation. The class of all dynamical systems is proper subclass of the class of all systems considered here 2. InFig.…”

mentioning

confidence: 99%

Multivaluedness in Networks: Theory

Wyk¹

2020

Preprint

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<div><div>This brief note reports the fundamental phenomenon of implicit multivaluedness exhibited from one output to the other of two node-systems with a common input—referred to as counter-cascaded1 systems—under the appropriate conditions. The novel concepts of immanence and transcendence are introduced upon which the formulation and prove of a necessary and sufﬁcient condition for multivaluedness are based; this is the main result of this note. Next, subsequent consequences of this result are presented. Among these is the fact that this result also holds for cascaded generalized systems. </div><div><br></div><div>The novel application of structural complexity reduction in directed networks presented next, demonstrates the utility of multivaluedness and is itself a contribution to the theory of signals and systems.</div><div><br></div><div>The signiﬁcance of the work presented here is that it contributes toward the theory of systems and networks as well as toward the arsenal of tools for studying networks.</div></div>

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Advances in Network Controllability

Cited by 112 publications

References 96 publications

Towards Optimal Robustness of Network Controllability: An Empirical Necessary Condition

Towards Optimal Robustness of Network Controllability: An Empirical Necessary Condition

Controllability of Directed Networked MIMO Systems With Heterogeneous Dynamics

Multivaluedness in Networks: Theory

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