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|Title: ||Synchronization analysis and control for complex dynamical networks|
|Other Titles: ||Fu za dong tai wang luo de tong bu fen xi yu kong zhi|
|Authors: ||Lu, Jianquan (盧劍權)|
|Department: ||Department of Mathematics|
|Degree: ||Doctor of Philosophy|
|Issue Date: ||2009|
|Publisher: ||City University of Hong Kong|
|Subjects: ||System analysis.|
|Notes: ||CityU Call Number: QA402 .L8 2009|
ix, 236 leaves : ill. 30 cm.
Thesis (Ph.D.)--City University of Hong Kong, 2009.
Includes bibliographical references (leaves -236)
|Abstract: ||Complex dynamical networks (CDNs) are ubiquitous in our real world, ranging from
biological, social, to man-made networks. Many interesting phenomena can be observed
in CDNs. Among them, synchronization has been a hot research topic in recent
years due to its potential applications. Synchronization emerges from the interconnections
of CDNs, but the final synchronous state is difficult to predict. However, for many
social, biological and physical dynamical networks, there is a common requirement to
regulate the final behavior of large ensembles of interacting units. It is desirable to
design controllers to force the unpredicted final synchronous state to certain required
objective states. Hence, there is a great demand to study synchronization behavior and
the control of CDNs.
There are some common phenomena in many evolutionary networks including
communication delays, switching topology, signal noise and impulsive effects. This
thesis presents our research and developments on the corresponding concerned issues
of synchronization analysis and the control problem of CDNs. Three classes of dynamical
networks with delay-coupling, switched structures and impulsive signals are
respectively presented. We are mainly concerned with the following problems: (a) synchronization
criteria of different kinds of dynamical networks; (b) the stabilization of
dynamical networks via different kinds of controllers; (c)the stabilization of dynamical
networks under performance constraint; (d) and impulsive dynamical networks.
For problem (a), synchronization criteria are derived to verify whether synchronization
of state-coupled and delay-coupled dynamical networks can be achieved. The
synchronizability of dynamical networks is also discussed. The constraint that the
coupling configuration matrix is symmetric and irreducible, which is frequently used in other literature, is removed.
For problem (b), adaptive controllers and pinning state-feedback control are, respectively,
designed for the stabilization of various kinds of dynamical networks. The
minimum number of pinning controllers is used to force the CDNs into certain objective
For problem (c), we investigate the dynamical network with both intrinsic disturbance
of single node and communication noise over the network connections. Hinfinity
controller is used for the exponential stabilization of dynamical network, and
the prescribed performance constraint is simultaneously satisfied.
For problem (d), there are two kinds of opposite impulses: synchronizing impulse
and desynchronizing impulse. We derive unified criteria to study the synchronization
of CDNs under the effects of synchronizing or desynchronizing impulses. Single impulsive
controller is designed to stabilize impulsive dynamical networks.
The main contributions of this thesis are listed as follows: (i) our results are available
for large-scale dynamical networks; (ii) diverse delays are verified to be quite
robust against the consensus of multi-agent systems; (iii) single impulsive controller
is designed for the stabilization of CDNs; (iv) the minimum number of pinning controllers
is obtained; (v) and unified criteria are proposed for the synchronization of
CDNs with synchronizing or desynchronizing impulses.|
|Online Catalog Link: ||http://lib.cityu.edu.hk/record=b2374859|
|Appears in Collections:||MA - Doctor of Philosophy |
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