With the help of rapidly advancing communication technology, control systems
are increasingly integrated via communication networks. Networked control systems
(NCSs) bring significant advantages such as flexible and scalable structures, easy
implementation and maintenance, and efficient resources distribution and allocation.
NCSs empowers to finish some complicated tasks using some relatively simple systems
in a collaborated manner. However, there are also some challenges and constraints
subject to the imperfection of communication channels. In this thesis, the stabilization
problems and the performance limitation problems of control systems subject to
networked-induced constraints are studied.
Overall, the thesis mainly includes two parts: 1) Consensus and consensusability
of multi-agent systems (MASs); 2) Delay margins of NCSs. Chapter 2 and Chapter 3
deal with the consensus problems of MASs, which aim to properly design the control
protocols to ensure the state convergence of all the agents. Chapter 4 and Chapter 5
focus on the consensusability analysis, exploring how the dynamics of the agents and
the networked induced constraints impact the overall systems for achieving consensus.
Chapter 6 pays attention to the delay margins of discrete-time linear time-invariant
(LTI) systems, studying how the dynamics of the plants limit the time delays that
can be tolerated by LTI controllers.
In Chapter 2, the leader-following consensus problem of MASs with general linear
dynamics and arbitrary switching topologies is considered. The MAS with arbitrary
switching topologies is formulated as a switched system. Then the leaderfollowing
consensus problem is transformed to the stability problem of the corresponding
switched system. A necessary and sufficient consensus condition is derived.
The condition is also extended to MASs with time-varying delays.
In Chapter 3, the consensus problem of MASs with general linear dynamics is
studied. Motivated by the multiple-input multiple-output (MIMO) communication
technique, a general framework is considered in which different state variables are
exchanged in different independent communication topologies. This novel framework
could improve the control system design flexibility and potentially improve the system
performance. Fully distributed consensus protocols are proposed and analyzed for
the settings of fixed and switching multiple topologies. The protocols can be applied
using only local information. And the control gains can be designed depending on
the dynamics of the individual agent. By transforming the overall MASs into cascade
systems, necessary and sufficient conditions are provided to guarantee the consensus
under fixed and switching state-variables-dependent topologies, respectively.
Chapter 4 investigates the consensusability problem for MASs with time-varying
delays. The bounded delays can be arbitrarily fast time-varying. The communication
topology is assumed to be undirected and fixed. Considering general linear dynamics
under average state protocols, the consensus problem is then transformed into a
robust control problem. Sufficient frequency domain criteria are established in terms
of small-gain theorem by analyzing the delay dependent gains for both continuoustime
and discrete-time systems. The controller synthesis problems can be solved by
applying the frequency domain design methods.
The consensusablity problem of general linear MASs considering directed topologies
are explored from a frequency domain perspective in Chapter 5. By investigating
the properties of Laplacian spectra, a consensus criterion is established based on the
stability of several complex weighted closed-loop systems. Furthermore, for singleinput
MASs, frequency domain consensusability criteria are proposed on the basis of
the stability margins, which depend on the H∞ norm of the complementary sensitivity
function determined by the agents’ unstable poles. The corresponding design
procedure is also developed.
Chapter 6 studies the delay margin problem of discrete-time LTI systems. For
general LTI plants with multiple unstable poles and nonminimum phase zeros, we
employ analytic function interpolation and rational approximation techniques to derive
bounds on delay margins. Readily computable and explicit lower bounds are
found by computing the real eigenvalues of a constant matrix, and LTI controllers can
be synthesized based on the H∞ control theory to achieve the bounds. The results
can be also consistently extended to the case of systems with time-varying delays.
For first-order unstable plants, we also obtain bounds achievable by proportionalintergral-
derivative (PID) controllers, which are of interest to PID control design and
implementation. It is worth noting that unlike its continuous-time counterpart, the
discrete-time delay margin problem being considered herein constitutes a simultaneous
stabilization problem, which is known to be rather difficult. While previous work
on the discrete-time delay margin led to negative results, the bounds developed in
this chapter provide instead a guaranteed range of delays within which the delayed
plants can be robustly stabilized, and in turn solve the special class of simultaneous
stabilization problems in question.
Finally, in Chapter 7, the thesis is summarized and some future research topics
are also presented. / Graduate
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/8901 |
| Date | 21 December 2017 |
| Creators | Chen, Yuanye |
| Contributors | Shi, Yang |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
| Rights | Available to the World Wide Web |
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