Pinning Complex Networks by a Single Controller
By Tianping Chen, Xiwei Liu, Wenlian Lu. IEEE Transactions on Circuits and Systems Part 1: Regular Papers, 2006
1,040 citations recorded by the source corpus.
In this paper, without assuming symmetry, irreducibility, or linearity of the couplings, we prove that a single controller can pin a coupled complex network to a homogenous solution. Sufficient conditions are presented to guarantee the convergence of the pinning process locally and globally. An effective approach to adapt the coupling strength is proposed. Several numerical simulations are given to verify our theoretical analysis.
Subfields: Computer Networks and Communications, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/1d296469d3f154b3b2866af7c94823203305dd24
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computer Networks and Communications
In Statistical and Nonlinear Physics
Citations in the corpus
- Cluster Synchronization in Directed Networks Via Intermittent Pinning Control (2011, methodology): “For example, [31], [52] gave the centralized adaptive method, while [53]– [57] presented various decentralized approaches, like node-based strategy, edge-based strategy, edge-snapping, etc.”
- Distributed leader-follower flocking control for multi-agent dynamical systems with time-varying velocities (2010, background): “To reduce the number of informed agents, some local feedback injections are applied to only a small percentage of agents, which is known as pinning feedback [13,36].”
- Synchronization of Complex Networks via Aperiodically Intermittent Pinning Control (2015, methodology): “If only a small fraction of network nodes are controlled, then it is called the pinning control, see [10]–[15].”
- Synchronization of Coupled Reaction-Diffusion Neural Networks with Time-Varying Delays via Pinning-Impulsive Controller (2013, background): “of complex network (see [8], [9], [10], [11], and [12]), has been extensively studied (see [13], [14], [15], [16], and [17]).”
- Control Principles of Complex Networks (2015, background): “For a more general desired trajectory, it has been shown that a single feedback controller can pin a complex network to a homogenous solution, without assuming symmetry, irreducibility, or linearity of the couplings (Chen et al., 2007).”
- Sampled-Data Synchronization Control of Dynamical Networks With Stochastic Sampling (2012, background): “The synchronization problem has recently been paid a great deal of efforts and some effective synchronization control schemes have been proposed for a variety of non-synchronous networks [1,6,15,17,18,20,21,23,25].”
- Cluster consensus control of generic linear multi-agent systems under directed topology with acyclic partition (2013, methodology): “By exploring some interesting properties of directed acyclic graphs together with a mixture of findings from graphic theory, matrix analysis theory, Lyapunov method, and pinning control techniques (Chen et al., 2007; Qin, Zheng, & Gao, 2011b), we can prove that the cluster consensus behavior of gene”
- Synchronization Control for Nonlinear Stochastic Dynamical Networks: Pinning Impulsive Strategy (2012, methodology): “Pinning state feedback controllers were first proposed to control multi-mode laser systems in [28], and have recently been used for the synchronization of complex networks by controlling a small fraction of nodes [19], [20], [22].”
- Distributed Consensus Filtering in Sensor Networks (2009, neutral): “Lemma 1 [27]: If A = (aij)N×N is irreducible, aij = aji ≥ 0, for i = j, and ∑N j=1 aij = 0, for all i = 1, 2, .”
- Synchronization via Pinning Control on General Complex Networks (2013, methodology): “The pinning strategy is applied on a small fraction δ (0 < δ < 1) of vertices in the network [7, 54, 38].”
- On H ∞ and H 2 performance regions of multi-agent systems ✩ (2011, background): “Thus, the positive definiteness of Lm associated with a connected graph follows directly from either Lemma 1 in Chen, Liu, and Lu (2007) or Lemma 3 in Hong et al. (2006).”
- Distributed control gains design for consensus in multi-agent systems with second-order nonlinear dynamics (2013, background): “There exist nonnegative constants ρ1 and ρ2 such that ∥f (x, v, t) − f (y, z, t)∥ ≤ ρ1∥x − y∥ + ρ2∥v − z∥, ∀x, y, v, z ∈ Rn. Assumption 1 is the so-called QUAD condition on vector fields (Chen et al., 2007).”
- On Pinning Synchronization of Directed and Undirected Complex Dynamical Networks (2010, methodology): “measure the quality of the pinning process [14].”