Adaptive Iterative Learning Control for Nonlinearly Parameterized Systems with Unknown Time-Varying Delays

다국어 초록 (Multilingual Abstract)

First of all, an adaptive iterative learning control strategy is developed for a class of nonlinearly parameterized systems with two unknown time-varying parameters and one unknown time-varying delay. The proposed control law includes a PID-type feedback term in time domain and an adaptive learning term used to estimate the unknown time-varying vector in iteration domain. By constructing a Lyapunov-Krasovskii-like composite energy function, we prove the stability of the closed-loop system and the convergence of the tracking error. Then, the design idea is further extended to a broader class of systems with mixed parameters in which the unknown time-invariant vector is estimated by a PI-type learning law in time domain. The simulation results, for a time-delay chaotic system, confirm the effectiveness of the proposed control scheme.

참고문헌 (Reference)

1 D.H.Owens, "Universal iterative learning control using adaptive high gain feedback" 7 (7): 383-388, 1993

2 A. Tayebi, "Unified adaptive iterative learning control framework for uncertain nonlinear systems" 52 (52): 1907-1913, 2007

3 Y. P. Tian, "Robust learning control for a class of nonlinear systems with periodic and aperiodic uncertainties" 39 (39): 1957-1966, 2003

4 W. E. Dixon, "Repetitive learning control: a Lyapunov -based approach" 50 (50): 1349-1354, 2005

5 Ali Madady, "PID Type Iterative Learning Control with Optimal Gains" 제어·로봇·시스템학회 6 (6): 194-203, 2008

6 H. F. Chen, "Output tracking for nonlinear stochastic systems by iterative learning control" 49 (49): 583-588, 2004

7 J. X. Xu, "On repetitive learning control for periodic tracking tasks" 51 (51): 1842-1848, 2006

8 J. X. Xu, "On iterative learning from different tracking tasks in the presence of timevarying uncertainties" 34 (34): 589-597, 2004

9 J. X. Xu, "On initial conditions in iterative learning control" 50 (50): 1349-1354, 2005

10 S.S.Saab, "On a discrete-time stochastic learning control algorithm" 46 (46): 1333-1336, 2001

11 J. X. Xu, "Observer based learning control for a class of nonlinear systems with timevarying parametric uncertainties" 49 (49): 275-281, 2005

12 M. French, "Non-linear iterative learning by an adaptive Lyapunov technique" 73 (73): 840-850, 2000

13 J. X. Xu, "Linear and Nonlinear Iteration Learning Control, Lecture Notes in Control and Information Sciences" Springer-Verlag 2003

14 Jianming Xu, "LMI-Based Synthesis of Robust Iterative Learning Controller with Current Feedback for Linear Uncertain Systems" 제어·로봇·시스템학회 6 (6): 171-179, 2008

15 R. W. Longman, "Iterative learning control and repetitive control for engineer practice" 73 (73): 930-954, 2000

16 K. L. Moor, "Iterative Learning Control for Deterministic Systems, Advances in Industrial Control" Springer-Verlag 1993

17 J. K. Hale, "Introduction to Functional Differential Equations" Springer-Verlay 1993

18 W. G. Seo, "Intelligent learning control for a class of nonlinear dynamic systems" 146 (146): 165-170, 2000

19 P. Jiang, "Indirect iterative learning control for a discrete visual servo without a camera-robot model" 37 (37): 1083-4419, 2007

20 도태용, "Feedback-Based Iterative Learning Control for MIMO LTI Systems" 제어·로봇·시스템학회 6 (6): 269-277, 2008

21 Y. C. Wang, "Direct adaptive iterative learning control of nonlinear systems using an output-recurrent fuzzy neural network" 34 (34): 1348-1359, 2004

22 H.Wu, "Design of iterative learning controllers for linear discrete systems with multiple time delays" 126 (126): 1138-1143, 2006

23 K. H. Park, "Design of an iterative learning controller for a class of linear dynamic systems with time delay" 145 (145): 507-512, 1998

24 A.Tayebi, "Analysis of two particular iterative learning control schemes in frequency and time domains" 43 (43): 1565-1572, 2007

25 Y. Chen, "Analysis of a highorder iterative learning control algorithm for uncertain nonlinear systems with state delays" 34 (34): 345-353, 1998

26 J. X. Xu, "Adaptive robust iterative learning control with dead zone scheme" 36 (36): 91-99, 2000

27 M. Sun, "Adaptive repetitive learning control of robotic manipulators without the requirement for initial repositioning" 22 (22): 563-568, 2006

28 B. H. Park, "Adaptive learning control of uncertain robotic systems" 65 (65): 725-744, 1996

29 W.S.Chen, "Adaptive learning control of linear systems with completely unknown time delays" 6 (6): 177-185, 2009

30 J. Y. Choi, "Adaptive iterative learning control of uncertain robotic systems" 147 (147): 217-223, 2000

31 A.Tayebi, "Adaptive iterative learning control for robot manipulators" 40 (40): 1195-1203, 2004

32 T. Y. Kuc, "Adaptive PID learning control of robot manipulators" 36 (36): 717-725, 2000

33 J.X.Xu, "A new periodic adaptive control approachfor time-varying parameters with known periodicity" 49 (49): 579-583, 2004

34 J. X. Xu, "A composite energy function- based learning control approach for nonlinear systems with time-varying parametric uncertainties" 47 (47): 1940-1945, 2002

35 X. D. Li, "2-D system theory based iterative learning control for linear continuous systems with time delays" 52 (52): 1421-1430, 2005