Minimum structural controllability problems of complex networks

et al. 2020

IEEE Access

Structural controllability of complex networks has been an attractive research area, and Minimum Inputs Theorem was proposed to identify the minimum driver nodes for complex networks with one-dimensional node dynamics. Then, the Minimum Inputs Theorem was extended to the complex network with multidimensional node dynamics by looking the multidimensional node as a subnetwork. However, when the structures of these subnetworks possess the root Strongly Connected Components that have perfect matching, the minimum driver nodes of these subnetworks are not sufficient to guarantee the full control, and some extra nodes are needed to be controlled. Therefore, in this paper, we study the structural controllability of complex networks with multidimensional node dynamics whose corresponding subnetworks possess such root Strongly Connected Components. First, we apply the Maximum Matching principle to the network topology to obtain which subnetworks we need to control. Then, an algorithm is proposed to identify a feasible minimum controlled node set of the subnetwork. Finally, by analyzing the structural features of the whole network and synthetically applying the proposed algorithm, Maximum Matching principle and Graphical Approach, a flowchart is given for identifying the minimum controlled node set of the whole network. By duality, the above results can also apply to the structural observability problem of such complex networks. INDEX TERMS Complex networks, multidimensional node dynamics, perfect matching, root strongly connected components, structural controllability.

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Structural Controllability for a Class of Complex Networks With Root Strongly Connected Components

et al. 2020

IEEE Access

“…With deeper understanding of the controllability of complex networks [18][19][20][21][22][23][24][25][26], more scholars have begun to explore the ability to control complex networks through various indicators. For example, Liu et al [18] addressed the structural controllability of arbitrary complex directed networks, identifying a minimal set of driver nodes that can guide the system to any desired state.…”

Section: Introductionmentioning

confidence: 99%

“…Jia et al [20] proposed the concept of node control capability in the further study; that is, the possibility of node becoming a driving node was calculated. Many research works have been published under the theoretical framework of structural controllability [21][22][23][24][25][26]. However, these quantitative controllability methods only roughly measure the dimensionality of controllable subsystems; they could not better distinguish the controllability of systems with the same number of dimensions of controllable subsystems.…”

Section: Introductionmentioning

confidence: 99%

Quantitative Controllability Index of Complex Networks

Advances in Mathematical Physics

Zhang

Han

et al. 2018

In this paper, the controllability issue of complex network is discussed. A new quantitative index using knowledge of control centrality and condition number is constructed to measure the controllability of given networks. For complex networks with different controllable subspace dimensions, their controllability is mainly determined by the control centrality factor. For the complex networks that have the equal controllable subspace dimension, their different controllability is mostly determined by the condition number of subnetworks’ controllability matrix. Then the effect of this index is analyzed based on simulations on various types of network topologies, such as ER random network, WS small-world network, and BA scale-free network. The results show that the presented index could reflect the holistic controllability of complex networks. Such an endeavour could help us better understand the relationship between controllability and network topology.

“…However, Olshevsky [28 ] has recently investigated the minimum structural controllability and proposed an algorithm to identifying MSS in polynomial time. In addition, Yin and Zhang [29 ] apply the linear integer programming method to study the minimum structural controllability of networks. In this paper, we develop a novel algorithm which formulates the problem of identifying an MSS as a minimum‐cost maximum flow problem, which can be solved in polynomial time.…”

Section: Introductionmentioning

confidence: 99%

Minimum steering node set of complex networks and its applications to biomolecular networks

et al. 2016

IET syst. biol.

Many systems of interests in practices can be represented as complex networks. For biological systems, biomolecules do not perform their functions alone but interact with each other to form so-called biomolecular networks. A system is said to be controllable if it can be steered from any initial state to any other final state in finite time. The network controllability has become essential to study the dynamics of the networks and understand the importance of individual nodes in the networks. Some interesting biological phenomena have been discovered in terms of the structural controllability of biomolecular networks. Most of current studies investigate the structural controllability of networks in notion of the minimum driver node sets (MDSs). In this study, the authors analyse the network structural controllability in notion of the minimum steering node sets (MSSs). They first develop a graph-theoretic algorithm to identify the MSS for a given network and then apply it to several biomolecular networks. Application results show that biomolecules identified in the MSSs play essential roles in corresponding biological processes. Furthermore, the application results indicate that the MSSs can reflect the network dynamics and node importance in controlling the networks better than the MDSs.