Fractional uncertainties are involved in many practical systems. Currently, there is a lack of research results about such general class of nonlinear systems in the context of learning control. This paper presents a Lyapunov-synthesis approach to repetitive learning control (RLC) being unified due to the use of the direct parametrization and adaptive bounding techniques. To effectively handle fractional uncertainties, the estimation method for such uncertainties is elaborated to facilitate the controller design and convergence analysis. Its novelty lies in the less requirement for the knowledge about the system undertaken. Unsaturated- and saturated-learning algorithms are, respectively, characterized by which both the boundedness of the variables in the closed-loop system undertaken and the asymptotical convergence of the tracking error are established. Experimental results are provided to verify the effectiveness of the presented learning control.

References

References
1.
Tomizuka
,
M.
,
Tsao
,
T.-C.
, and
Chew
,
K.-K.
,
1989
, “
Analysis and Synthesis of Discrete-Time Repetitive Controllers
,”
ASME J. Dyn. Syst. Meas. Control
,
111
(
3
), pp.
353
358
.
2.
Arimoto
,
S.
,
1990
, “
Learning Control Theory for Robotic Motion
,”
Int. J. Adapt. Control Signal Process.
,
4
(
6
), pp.
543
564
.
3.
Longman
,
R. W.
,
2000
, “
Iterative Learning Control and Repetitive Control for Engineering Practice
,”
Int. J. Control
,
73
(
10
), pp.
930
954
.
4.
Bristow
,
D. A.
,
Tharayil
,
M.
, and
Alleyne
,
A. G.
,
2006
, “
A Survey of Iterative Learning Control
,”
IEEE Trans. Control Syst. Mag.
,
26
(
3
), pp.
96
114
.
5.
Wang
,
D.
,
Ye
,
Y.
, and
Zhang
,
B.
,
2014
,
Practical Iterative Learning Control With Frequency Domain Design and Sampled Data Implementation
,
Springer
,
Singapore
.
6.
Pipeleers
,
G.
, and
Moore
,
K. L.
,
2014
, “
Unified Analysis of Iterative Learning and Repetitive Controllers in Trial Domain
,”
IEEE Trans. Autom. Control
,
59
(
4
), pp.
953
965
.
7.
Sadegh
,
N.
,
Horowitz
,
R.
,
Kao
,
W.
, and
Tomizuka
,
M.
,
1990
, “
A Unified Approach to Design of Adaptive and Repetitive Controllers for Robotic Manipulators
,”
ASME J. Dyn. Syst. Meas. Control
,
112
(
4
), pp.
618
629
.
8.
Kuc
,
T.-Y.
,
Kwanghee
,
N.
, and
Lee
,
J.
,
1991
, “
An Iterative Learning Control of Robot Manipulators
,”
IEEE Trans. Rob. Autom.
,
7
(
6
), pp.
853
842
.
9.
Qu
,
Z.
,
Dorsey
,
J.
,
Dawson
,
D.
, and
Johnson
,
R.
,
1993
, “
Linear Learning Control of Robot Motion
,”
J. Rob. Syst.
,
10
(
1
), pp.
123
140
.
10.
Park
,
B.
,
Kuc
,
T.
, and
Lee
,
J.
,
1996
, “
Adaptive Learning Control of Uncertain Robotic Systems
,”
Int. J. Control
,
65
(
5
), pp.
725
744
.
11.
Qu
,
Z.
, and
Xu
,
J. X.
,
2002
, “
Model Based Learning Control and Their Comparisons Using Lyapunov Direct Method
,”
Asian J. Control
,
4
(
1
), pp.
99
110
.
12.
Xu
,
J. X.
,
2011
, “
A Survey on Iterative Learning Control for Nonlinear Systems
,”
Int. J. Control
,
84
(
7
), pp.
1275
1294
.
13.
French
,
M.
, and
Rogers
,
E.
,
2000
, “
Non-Linear Iterative Learning by an Adaptive Lyapunov Technique
,”
Int. J. Control
,
73
(
10
), pp.
840
850
.
14.
Sun
,
D.
, and
Mills
,
J. K.
,
1999
, “
Performance Improvement of Industrial Robot Trajectory Tracking Using Adaptive-Learning Scheme
,”
ASME J. Dyn. Syst. Meas. Control
,
121
(
2
), pp.
285
292
.
15.
Xu
,
L.
, and
Yao
,
B.
,
2001
, “
Adaptive Robust Repetitive Control of a Class of Nonlinear Systems in Normal Form With Applications to Motion Control of Linear Motors
,” IEEE/ASME International Conference on Advanced Intelligent Mechantronics (
AIM
), Como, Italy, July 8–12, pp.
527
532
.
16.
Xu
,
J. X.
, and
Tan
,
Y.
,
2002
, “
A Composite Energy Function-Based Learning Control Approach for Nonlinear Systems With Time-Varying Parametric Uncertainties
,”
IEEE Trans. Autom. Control
,
47
(
11
), pp.
1940
1945
.
17.
Dixon
,
W. E.
,
Zergeroglu
,
E.
,
Dawson
,
D. M.
, and
Costic
,
B. T.
,
2002
, “
Repetitive Learning Control: A Lyapunov-Based Approach
,”
IEEE Trans. Syst. Man Cybern., Part B
,
32
(
4
), pp.
538
545
.
18.
Sun
,
M.
, and
Ge
,
S. S.
,
2006
, “
Adaptive Repetitive Control for a Class of Nonlinearly Parametrized Systems
,”
IEEE Trans. Autom. Control
,
51
(
10
), pp.
1684
1688
.
19.
Tan
,
Y. H. H.
,
Dai
,
D. H.
, and
Xu
,
J. X.
,
2012
, “
Unified Iterative Learning Control Schemes for Nonlinear Dynamic Systems With Nonlinear Input Uncertainties
,”
Automatica
,
48
(
12
), pp.
3173
3182
.
20.
Tayebi
,
A.
, and
Chien
,
C. J.
,
2007
, “
A Unified Adaptive Iterative Learning Control Framework for Uncertain Nonlinear Systems
,”
IEEE Trans. Autom. Control
,
52
(
10
), pp.
1907
1913
.
21.
Qu
,
Z.
, and
Xu
,
J. X.
,
2002
, “
Asymptotic Learning Control for a Class of Cascaded Nonlinear Uncertain Systems
,”
IEEE Trans. Autom. Control
,
47
(
8
), pp.
1369
1376
.
22.
Chien
,
C. J.
,
2008
, “
A Combined Adaptive Law for Fuzzy Iterative Learning Control of Nonlinear Systems With Varying Control Tasks
,”
IEEE Trans. Fuzzy Syst.
,
16
(
1
), pp.
40
51
.
23.
Quan
,
Q.
, and
Cai
,
K. Y.
,
2011
, “
A Filtered Repetitive Controller for a Class of Nonlinear Systems
,”
IEEE Trans. Autom. Control
,
56
(
2
), pp.
399
405
.
24.
Qu
,
Z.
,
1998
,
Robust Control of Nonlinear Uncertain Systems
,
Wiley
,
New York
.
25.
Tian
,
Y.
, and
Yu
,
X.
,
2003
, “
Robust Learning Control for a Class of Nonlinear Systems With Periodic and a Periodic Uncertainties
,”
Automatica
,
39
(
11
), pp.
1957
1966
.
26.
Chen
,
W.
, and
Jiao
,
L.
,
2010
, “
Adaptive Tracking for Periodically Time-Varying and Nonlinearly Parameterized Systems Using Multilayer Neural Network
,”
IEEE Trans. Neural Networks
,
21
(
2
), pp.
345
351
.
27.
Li
,
X.
,
Huang
,
D.
,
Chu
,
B.
, and
Xu
,
J. X.
,
2016
, “
Robust Iterative Learning Control for Systems With Norm-Bounded Uncertainties
,”
Int. J. Robust Nonlinear Control
,
26
(
4
), pp.
697
718
.
28.
Marino
,
R.
, and
Tomei
,
P.
,
2009
, “
An Iterative Learning Control for a Class of Partially Feedback Linearizable Systems
,”
IEEE Trans. Autom. Control
,
54
(
8
), pp.
1991
1996
.
29.
Sun
,
M.
,
2009
, “
A Barbalat-Like Lemma With Its Application to Learning Control
,”
IEEE Trans. Autom. Control
,
54
(
9
), pp.
2222
2225
.
30.
Yang
,
Z.
,
Yam
,
S. C. P.
,
Li
,
L. K.
, and
Wang
,
Y.
,
2010
, “
Universal Repetitive Learning Control for Nonparametric Uncertainty and Unknown Control Gain Matrix
,”
IEEE Trans. Autom. Control
,
55
(
7
), pp.
1710
1715
.
31.
Jin
,
X.
,
Huang
,
D.
, and
Xu
,
J.-X.
,
2012
, “
Iterative Learning Control for Systems With Nonparametric Uncertainties Under Alignment Condition
,” 51st IEEE Conference on Decision and Control (
CDC
), Maui, HI, Dec. 10–13, pp.
3942
3947
.
32.
Huang
,
D.
,
Xu
,
J.-X.
,
Yang
,
S.
, and
Jin
,
X.
,
2015
, “
Observer Based Repetitive Learning Control for a Class of Nonlinear Systems With Non-Parametric Uncertainties
,”
Int. J. Robust Nonlinear Control
,
25
(
8
), pp.
1214
1229
.
33.
Sun
,
M.
,
Wang
,
Y.
, and
Wang
,
D.
,
2005
, “
Variable-Structure Repetitive Control: A Discrete-Time Strategy
,”
IEEE Trans. Ind. Electron.
,
52
(
2
), pp.
610
616
.
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