Browse > Article
http://dx.doi.org/10.5302/J.ICROS.2002.8.5.385

Takagi-Sugeno Fuzzy Model-Based Iterative Learning Control Systems: A Two-Dimensional System Theory Approach  

Chu, Jun-Uk (Dept.of Electronics Engineering, Kyungpook National University)
Lee, Yun-Jung (Dept.of Electronics Engineering, Kyungpook National University)
Park, Bong-Yeol (Dept.of Electronics Engineering, Kyungpook National University)
Publication Information
Journal of Institute of Control, Robotics and Systems / v.8, no.5, 2002 , pp. 385-392 More about this Journal
Abstract
This paper introduces a new approach to analysis of error convergence for a class of iterative teaming control systems. Firstly, a nonlinear plant is represented using a Takagi-Sugeno(T-S) fuzzy model. Then each iterative learning controller is designed for each linear plant in the T-S fuzzy model. From the view point of two-dimensional(2-D) system theory, we transform the proposed learning systems to a 2-D error equation, which is also established if the form of T-S fuzzy model. We analyze the error convergence in the sense of induced L$_2$-norm, where the effects of disturbances and initial conditions on 2-D error are considered. The iterative teaming controller design problem to guarantee the error convergence can be reduced to the linear matrix inequality problem. This method provides a systematic design procedure for iterative teaming controller. A simulation example is given to illustrate the validity of the proposed method.
Keywords
iterative learning control; Takigi-Sugeno fuzzy model; two-dimensional systems;
Citations & Related Records
연도 인용수 순위
  • Reference
1 S. Arimoto, S. Kawamura, and F. Miyazaki, 'Bettering operation of robots by learning,' Journal of Robotic Systems, vol. 1, no. 2, pp. 123-140, 1984   DOI
2 G. Heinzinger, D. Fenwick, B. Paden, and F. Miyazaki, 'Stability of learning control with disturbances and uncertain initial conditions,' IEEE Trans. Automat. Contr., vol. 37, no. 1, pp. 110-114, 1992   DOI   ScienceOn
3 H. S. Ahn, C. H. Choi, and K. B. Kim, 'Iterative learning control for a class of nonlinear systems,' Automatica, vol. 29, no. 6, pp. 1575-1578, 1993   DOI   ScienceOn
4 T. Y. Kuc, J. S. Lee, and K. Nam,'An iterative learning control theory for a class of nonlinear dynamics systems,' Automatica, vol. 28, no. 6, pp. 1215-1221, 1992   DOI   ScienceOn
5 A. R. E. Ahmed, 'On the stability of two-dimensional discrete systems,' IEEE Trans. Automat. Contr., vol. AC-25, no. 3, pp. 551-552, 1980   DOI
6 D. H. Owens and G. Munde, 'Error convergence in an adaptive iterative learning controller,' INT. J. Control, vol. 73, no. 10, pp. 851-857, 2000   DOI
7 C. Ham, Z. Qu, and J. Kaloust, 'Nonlinear learning control for a class of nonlinear systems,' Automatica, vol. 37, pp. 419-428, 2001   DOI   ScienceOn
8 H. S. Lee and Z. Bien, 'A note on convergence property of iterative learning controller with respect to sup norm,' Automatica, vol. 33, no. 8, pp. 1591-1593, 1997   DOI   ScienceOn
9 K. Tanaka, T. Ikeda, and H. O. Wang, 'Robust stabilization of a class of uncertain nonlinear systems via fuzzy control : quadratic stabilizability, control theory, and linear matrix inequalities,' IEEE Trans. Fuzzy Systems, vol. 4, no. 1, pp. 1-13, 1996   DOI   ScienceOn
10 H. O. Wang, K. Tanaka, and M. F. Griffin, 'An approach to fuzzy control of nonlinear systems : stability and design issues,' IEEE Trans. Fuzzy Systems, vol. 4, no. 1, pp. 14-23, 1996   DOI   ScienceOn
11 D. Goodman, 'Some stability properties of two-dimensional linear shift-invariant digital filters,' IEEE Trans. Circuits and Systems, vol. CAS-24, no. 4, pp. 201-206, 1977   DOI
12 J. A. Frueh and M. Q. Phan, 'Linear quadratic optimal learning control,' INT. J. Control, vol. 73, no. 10, pp. 832-839, 2000   DOI
13 J. J. Lee and J. W. Lee, 'Design of iterative learning controller with VCR servo system,' IEEE Trans. Consumer Electronics, vol. 39, no. 1, pp. 13-24, 1993   DOI   ScienceOn
14 M. French and E. Rogers, 'Non-linear iterative learning by an adaptive lyapunov technique, 'INT. J. Control, vol. 73, no. 10, pp. 840-850, 2000   DOI
15 R. P. Roesser, 'A discrete state-space model for linear image processing,' IEEE Trans. Automat. Contr., vol. AC-20, no. 1, pp. 1-10, 1975   DOI
16 Z. Geng, R. Carroll, and J. Xie, 'Two-dimensional model and algorithm analysis for a class of iterative learning control systems,' INT. J. Control, vol. 52, no. 4, pp. 833-862, 1990   DOI   ScienceOn
17 J. E. Kurek and M. B. Zaremba, 'Iterative learning control synthesis based 2-D system theory,' IEEE Trans. Automat. Contr., vol. 38, no. 1, pp. 121-125, 1993   DOI   ScienceOn
18 S. S. Saab, 'A discrete-time learning control algorithm for a class of linear time-invariant systems,' IEEE Trans. Automat. Contr., vol. 40, no. 6, pp. 1138-1142, 1995   DOI   ScienceOn
19 J. E. Kurek, 'Stability of nonlinear parameter-varying digital 2-D systems,' IEEE Trans. Automat. Contr., vol. 40, no. 8, pp. 1428-1432, 1995   DOI   ScienceOn