Gradient-Constrained Minimum Networks. III. Fixed Topology

The consensus problems of two situations for singular multi-agent systems with fixed topology are discussed: directed graph without spanning tree and the disconnected undirected graph. A sufficient and necessary condition is obtained by applying the stability theory and the system is reachable asymptotically. But for normal systems, this can’t occur in upper two situations. Finally a simulation example is provided to verify the effectiveness of our theoretical result.

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Fixed topology skeletons

Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662) ◽

10.1109/cvpr.2000.855792 ◽

2002 ◽

Cited By ~ 23

Author(s):

P. Golland ◽

W. Eric ◽

L. Grimson

Keyword(s):

Fixed Topology

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Impulsive Consensus for Leader-Following Multiagent Systems with Fixed and Switching Topology

Mathematical Problems in Engineering ◽

10.1155/2013/762861 ◽

2013 ◽

Vol 2013 ◽

pp. 1-10 ◽

Cited By ~ 3

Author(s):

Zhi-Wei Liu ◽

Zhi-Hong Guan ◽

Hong Zhou

Keyword(s):

Multiagent System ◽

Impulsive Control ◽

Sampling Period ◽

Switching Topology ◽

Sufficient Condition ◽

Leader Following ◽

Fixed Topology ◽

The Stability ◽

Sampling Instant ◽

Necessary And Sufficient

This paper studied the consensus problem of the leader-following multiagent system. It is assumed that the state information of the leader is only available to a subset of followers, while the communication among agents occurs at sampling instant. To achieve leader-following consensus, a class of distributed impulsive control based on sampling information is proposed. By using the stability theory of impulsive systems, algebraic graph theory, and stochastic matrices theory, a necessary and sufficient condition for fixed topology and sufficient condition for switching topology are obtained to guarantee the leader-following consensus of the multiagent system. It is found that leader-following consensus is critically dependent on the sampling period, control gains, and interaction graph. Finally, two numerical examples are given to illustrate the effectiveness of the proposed approach and the correctness of theoretical analysis.

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Pinning synchronization of coupled fractional-order time-varying delayed neural networks with arbitrary fixed topology

Neurocomputing ◽

10.1016/j.neucom.2020.03.029 ◽

2020 ◽

Vol 400 ◽

pp. 46-52 ◽

Cited By ~ 2

Author(s):

Peng Liu ◽

Minxue Kong ◽

Minglin Xu ◽

Junwei Sun ◽

Na Liu

Keyword(s):

Neural Networks ◽

Fractional Order ◽

Time Varying ◽

Delayed Neural Networks ◽

Fixed Topology

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LIA: A LOCATION-INDEPENDENT TRANSFORMATION FOR ASOCS ADAPTIVE ALGORITHM 2

International Journal of Neural Systems ◽

10.1142/s0129065796000622 ◽

1996 ◽

Vol 07 (05) ◽

pp. 639-653

Author(s):

GEORGE L. RUDOLPH ◽

TONY R. MARTINEZ

Keyword(s):

Adaptive Algorithm ◽

Concurrent Systems ◽

Local Information ◽

General Strategy ◽

Formal Description ◽

Learning Models ◽

Formal Definitions ◽

Network Output ◽

Fixed Topology ◽

Independent Transformation

Most Artificial Neural Networks (ANNs) have a fixed topology during learning, and often suffer from a number of short-comings as a result. ANNs that use dynamic topologies have shown the ability to overcome many of these problems. Adaptive Self-Organizing Concurrent Systems (ASOCS) are a class of learning models with inherently dynamic topologies. This paper introduces Location-Independent Transformations (LITs) as a general strategy for implementing learning models that use dynamic topologies efficiently in parallel hardware. An LIT creates a set of location-independent nodes, where each node computes its part of the network output independent of other nodes, using local information. This type of transformation allows efficient support for adding and deleting nodes dynamically during learning. In particular, this paper presents the Location-Independent ASOCS (LIA) model as an LIT for ASOCS Adaptive Algorithm 2. The description of LIA gives formal definitions for LIA algorithms. Because LIA implements basic ASOCS mechanisms, these definitions provide a formal description of basic ASOCS mechanisms in general, in addition to LIA.

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