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不确定线性分布参数系统的带遗忘因子的迭代学习控制
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不确定线性分布参数系统的带遗忘因子的迭代学习控制
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Research Article
Iterative Learning Control with Forgetting Factor for Linear
Distributed Parameter Systems with Uncertainty
Xisheng Dai,
1
Senping Tian,
2
Wenguang Luo,
1
and Yajun Guo
1
1
School of Electrical and Information Engineering, Guangxi University of Science and Technology, Liuzhou 545006, China
2
School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640, China
Received 1 November 2014; Accepted 2 December 2014; Published 18 December 2014
Academic Editor: Wuneng Zhou
Copyright © 2014 Xisheng Dai et al. is is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Iterative learning control is an intelligent control algorithm which imitates human learning process. Based on this concept, this
paper discussed iterative learning control problem for a class parabolic linear distributed parameter systems with uncertainty
coecients. Iterative learning control algorithm with forgetting factor is proposed and the conditions for convergence of algorithm
are established. Combining the matrix theory with the basic theory of distributed parameter systems gives rigorous convergence
proof of the algorithm. Finally, by using the forward dierence scheme of partial dierential equation to solve the problems, the
simulation results are presented to illustrate the feasibility of the algorithm.
1. Introduction
Iterative learning control (ILC) is an intelligent control
method for systems which perform tasks repetitively over
a nite time interval. Since the original work by Arimoto
et al. [1], in the last three decades, ILC has been constantly
studied. Currently, the iterative learning control (ILC) prob-
lem for lumped parameter systems which describes ordinary
dierential equations has been studied continuously, and very
rich theory results are obtained [2–5]. Meanwhile, owning
to the ILC method is also suitable to some systems which
possess model uncertainty and nonlinear characteristics, so
in practice ILC has also been widely applied; for example, ILC
has been applied successfully in industrial robots, intelligent
transportation systems, injection process, biomedical engi-
neering, aspects of steelmaking, and tobacco fermentation
systems and has obtained great economic benet [6–10]. e
main benet of ILC is that for the design of control law not
much information about the plant is required and it may
even be completely unknown, it only requires the tracking
references and input/output signals. However, the algorithm
is simple and eective [11–13].
Recently, iterative learning control problem of distributed
parameter systems described by partial dierential equa-
tions has become a hot research. In [14], the ILC method
was used on temperature control of the nonisothermal tur-
bulence chemical reactor which has a rst-order hyper-
bolic distributed parameter systems characteristics. Qu fur-
ther applied iterative learning control to a exible system
described by a class of second order hyperbolic equations
at in [15]; Zhao and Rahn discussed the ILC of distributed
parameter systems control problems in the material trans-
portation system [16], and its learning control laws act to the
system boundary. Based on the operator semigroup theory,
ChaoandhiscoauthorsgiveasucientconditionofP-
type and D-type learning algorithm for a class of parabolic
distributed parameter systems [17]. In [18], Cichy and his
coauthors used Crank-Nicholson discretization; ILC for par-
abolic distributed parameter systems is proposed. Dai and
his coauthors discussed nonlinear learning algorithms of dis-
tributed parameter systems by using vector diagram theory
and studied ILC of distributed parameter systems learning
control problems with state time delays [19–21]. Lately, Huang
andhiscoauthorsstudiedakindofsteady-stateiterative
learning control problem for a class of nonlinear distributed
parameter systems [22, 23].
On the other hand, ILC is a branch of the intelligent con-
trol with strict mathematical description, where one of its
basic research issues is to design learning algorithm and
Hindawi Publishing Corporation
Journal of Control Science and Engineering
Volume 2014, Article ID 508573, 7 pages
http://dx.doi.org/10.1155/2014/508573
weixin_38577378
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