作者：
Shang, Y.Northumbria Univ
Dept Comp & Informat Sci Newcastle Upon Tyne NE1 8ST Tyne & Wear England
Cooperative coordination in multi-agent systems has been a topic of interest in networked control theory in recent years. In contrast to cooperative agents, Byzantine agents in a network are capable to manipulate thei...
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Cooperative coordination in multi-agent systems has been a topic of interest in networked control theory in recent years. In contrast to cooperative agents, Byzantine agents in a network are capable to manipulate their data arbitrarily and send bad messages to neighbors, causing serious network security issues. This paper is concerned with resilient tracking consensus over a time-varying random directed graph, which consists of cooperative agents, Byzantine agents and a single leader. The objective of resilient tracking consensus is the convergence of cooperative agents to the leader in the presence of those deleterious Byzantine agents. We assume that the number and identity of the Byzantine agents are not known to cooperative agents, and the communication edges in the graph are dynamically randomly evolving. Based upon linear system analysis and a martingale convergence theorem, we design a linear discrete-time protocol to ensure tracking consensus almost surely in a purely distributed manner. Some numerical examples are provided to verify our theoretical results.
Let F-q be a finite field with q elements, n >= 2 a positive integer, V-0 a n-dimensional vector space over F-q and T-0 the set of all linear functionals from V-0 to F-q. Let V = V-0 \ {0} and T = T-0 \ {0}. The li...
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Let F-q be a finite field with q elements, n >= 2 a positive integer, V-0 a n-dimensional vector space over F-q and T-0 the set of all linear functionals from V-0 to F-q. Let V = V-0 \ {0} and T = T-0 \ {0}. The linear functional graph of V-0 dented by F(V), is an undirected bipartite graph, whose vertex set V is partitioned into two sets as V = V boolean OR T and two vertices v is an element of V and f is an element of T are adjacent if and only if f sends v to the zero element of F-q (i.e. f (v) = 0). In this paper, the structure of all automorphisms of this graph is characterized and formalized. Also the cardinal number of automorphisms group for this graph is determined.
We investigate the effects of structural perturbations on the networks ability to synchronize. We establish a classification of directed links according to their impact on synchronizability. We focus on adding directe...
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We investigate the effects of structural perturbations on the networks ability to synchronize. We establish a classification of directed links according to their impact on synchronizability. We focus on adding directed links in weakly connected networks having a strongly connected component acting as driver. When the connectivity of the driver is not stronger than the connectivity of the slave component, we can always make the network strongly connected while hindering synchronization. On the other hand, we prove the existence of a perturbation which makes the network strongly connected while increasing the synchronizability. Under additional conditions, there is a node in the driving component such that adding a single link starting at an arbitrary node of the driven component and ending at this node increases the synchronizability.
Taking a Fiedler's result on the spectrum of a matrix formed from two symmetric matrices as a motivation, a more general result is deduced and applied to the determination of adjacency and Laplacian spectra of gra...
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Taking a Fiedler's result on the spectrum of a matrix formed from two symmetric matrices as a motivation, a more general result is deduced and applied to the determination of adjacency and Laplacian spectra of graphs obtained by a generalized join graph operation on families of graphs (regular in the case of adjacency spectra and arbitrary in the case of Laplacian spectra). Some additional consequences are explored, namely regarding the largest eigenvalue and algebraic connectivity. (C) 2012 Elsevier B.V. All rights reserved.
Let F-q be a finite field of q elements, V an n-dimensional vector space over F-q. Recently, Wang et al. in [Automorphisms and domination numbers of transformation graphs over vector spaces. linear Multilinearalgebra...
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Let F-q be a finite field of q elements, V an n-dimensional vector space over F-q. Recently, Wang et al. in [Automorphisms and domination numbers of transformation graphs over vector spaces. linear Multilinearalgebra. 2019;67:1350-1363] defined a graph Gamma'(V) with vertex set T boolean OR W, where 'T is the set of all nonzero singular linear transformations over V and W is the set of all nontrivial subspaces of V, and there is an undirected edge between A is an element of T and W is an element of W if and only if A maps W to the zero space, that is A(W) = algebra. In the end of Wang et al. [Automorphisms and domination numbers of transformation graphs over vector spaces. linear Multilinearalgebra. 2019;67:1350-1363], the authors posed an open problem: Characterizing the domination number and the automorphisms of Gamma'(V). In the present article, we solve this problem completely.
Let F-q be a finite field of q elements, V-0 an n-dimensional vector space over F-q and T-0 the set of all linear transformations of V-0. Let V = V-0 \ {0} and let T be the subset of T-0 consisting of all irreversible...
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Let F-q be a finite field of q elements, V-0 an n-dimensional vector space over F-q and T-0 the set of all linear transformations of V-0. Let V = V-0 \ {0} and let T be the subset of T-0 consisting of all irreversible nonzero linear transformations on V-0. The transformation graph of V-0, written as Gamma(V), is a bipartite graph, whose vertex set V is partitioned into two colouring sets as V = T boolean OR V and there is an undirected edge between A is an element of T and v is an element of V if and only if A maps v to the zero vector, that is A(v) = 0. In this paper, the domination number and the automorphisms of Gamma(V) are determined.
We consider the real three-dimensional Euclidean Jordan algebra associated to a strongly regular graph. Then, the Krein parameters of a strongly regular graph are generalized and some generalized Krein admissibility c...
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We consider the real three-dimensional Euclidean Jordan algebra associated to a strongly regular graph. Then, the Krein parameters of a strongly regular graph are generalized and some generalized Krein admissibility conditions are deduced. Furthermore, we establish some relations between the classical Krein parameters and the generalized Krein parameters.
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