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This study considers the convergence analysis approach to iterative learning control (ILC) which is achieved based on two-dimensional (2D) Roesser systems. Stability results are proposed for 2D Roesser systems when they are subject to varying parameters with respect to independent time and iteration axes. It is shown that the convergence analysis of ILC for a class of non-linear systems can be performed based on the established stability results of varying 2D Roesser systems. Moreover, the presented convergence results of ILC can work with sufficient robustness against iteration-varying initial state shifts. Illustrative simulations are included to verify the established convergence results of ILC for non-linear systems.
References
-
-
1)
-
24. Horn, R.A., Johnson, C.R.: ‘Matrix analysis’ (Cambridge University Press, Cambridge, 1985).
-
2)
-
23. Kaczorek, T.: ‘Two-dimensional linear systems’ (Springer, Berlin, 1985).
-
3)
-
J. Shi ,
F. Gao ,
T.J. Wu
.
Robust design of integrated feedback and iterative learning control of a batch process based on a 2D Roesser system.
J. Process Control
,
8 ,
907 -
924
-
4)
-
14. Galkowski, K., Rogers, E., Xu, S., Lam, J., Owens, D.H.: ‘LMIs-a fundamental tool in analysis and controller design for discrete linear repetitive processes’, IEEE Trans. Circuits Syst. Part I, Fundam. Theory Appl., 2002, 49, (6), pp. 768–778 (doi: 10.1109/TCSI.2002.1010032).
-
5)
-
D. Meng ,
Y. Jia ,
J. Du ,
F. Yu
.
Necessary and sufficient stability condition of LTV iterative learning control systems using a 2-D approach.
Asian J. Control
,
1 ,
25 -
37
-
6)
-
S.A. Saab
.
Discrete-time learning control algorithm for a class of linear time-invariant systems.
IEEE Trans. Autom. Control
,
1138 -
1142
-
7)
-
2. Hladowski, L., Galkowski, K., Rogers, E., Owens, D.H.: ‘On controllability and control laws for discrete linear repetitive processes’, Int. J. Control, 2010, 83, (1), pp. 66–73 (doi: 10.1080/00207170903100206).
-
8)
-
Z. Geng ,
R. Carroll ,
J. Xie
.
Two-dimensional model and algorithm analysis for a class of iterative learning control systems.
Int. J. Control
,
4 ,
833 -
862
-
9)
-
21. Liu, Y., Jia, Y.: ‘Robust formation control of discrete-time multi-agent systems by iterative learning approach’, Int. J. Syst. Sci., , 2015, 46, (4), pp. 625–633 (doi: 10.1080/00207721.2013.793781).
-
10)
-
25. Rugh, W.J.: ‘Linear system theory’ (Prentice-Hall, Upper Saddle River, NJ, 1996).
-
11)
-
D.A. Bristow ,
M. Tharayil ,
A.G. Alleyne
.
A survey of iterative learning control.
IEEE Control Syst. Mag.
,
3 ,
96 -
114
-
12)
-
10. Xu, J.-X.: ‘A survey on iterative learning control for nonlinear systems’, Int. J. Control, 2011, 84, (7), pp. 1275–1294 (doi: 10.1080/00207179.2011.574236).
-
13)
-
D. Meng ,
Y. Jia ,
J. Du ,
S. Yuan
.
Robust discrete-time iterative learning control for nonlinear systems with varying initial state shifts.
IEEE Trans. Autom. Control
,
11 ,
2626 -
2631
-
14)
-
17. Meng, D., Jia, Y., Du, J., Yu, F.: ‘Data-driven control for relative degree systems via iterative learning’, IEEE Trans. Neural Netw., 2011, 22, (12), pp. 2213–2225 (doi: 10.1109/TNN.2011.2174378).
-
15)
-
20. Meng, D., Jia, Y., Du, J., Zhang, J., Li, W.: ‘Formation learning algorithms for mobile agents subject to 2-D dynamically changing topologies’. Proc. of the American Control Conf., Washington, DC, USA, 17–19 June 2013, pp. 5172–5177.
-
16)
-
Y. Fang ,
T.W.S. Chow
.
2-D analysis for iterative learning controller for discrete-time systems with variable initial conditions.
IEEE Trans. Circuits Syst., I Fundam. Theory Appl.
,
5 ,
722 -
727
-
17)
-
3. Emelianova, J., Pakshin, P., Galkowski, K., Rogers, E.: ‘Vector Lyapunov function based stability of a class of applications relevant 2D nonlinear systems’. Proc. of the 19th IFAC World Congress, Cape Town, South Africa, 24–29 August 2014, pp. 8247–8252.
-
18)
-
16. Wu, L., Wang, Z., Gao, H., Wang, C.: ‘Robust H∞ filtering for uncertain two-dimensional discrete systems with state delays’, Signal Process., 2007, 87, (9), pp. 2213–2230 (doi: 10.1016/j.sigpro.2007.03.002).
-
19)
-
L. Wu ,
H. Gao
.
Sliding mode control of two-dimensional systems in Roesser model.
IET Control Theory Appl.
,
4 ,
352 -
364
-
20)
-
L. Wu ,
X. Yao ,
W. Zheng
.
Generalized H2 fault detection for two-dimensional Markovian jump systems.
Automatica
,
8 ,
1741 -
1750
-
21)
-
H.-S. Ahn ,
Y. Chen ,
K.L. Moore
.
Iterative learning control: brief survey and categorization.
IEEE Trans. Syst. Man Cybern. C
,
6 ,
1099 -
1121
-
22)
-
22. Meng, D., Jia, Y., Du, J., Zhang, J.: ‘On iterative learning algorithms for the formation control of nonlinear multi-agent systems’, Automatica, 2014, 50, (1), pp. 291–295 (doi: 10.1016/j.automatica.2013.11.009).
-
23)
-
X.-D. Li ,
J.K.L. Ho ,
T.W.S. Chow
.
Iterative learning control for linear time-variant discrete systems based on 2-D system theory.
IEE Proc. Control Theory Appl.
,
1 ,
13 -
18
-
24)
-
J.E. Kurek ,
M.B. Zaremba
.
Iterative learning control synthesis based on 2-D system theory.
IEEE Trans. Autom. Control
,
121 -
125
-
25)
-
L. Wu ,
P. Shi ,
H. Gao ,
C. Wang
.
ℋ∞ filtering for 2D Markovian jump systems.
Automatica
,
7 ,
1849 -
1858
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