Abstract
A novel output-feedback adaptive learning control approach is developed for a class of linear time-delay systems. Three kinds of uncertainties: time delays, number of time delays, and system parameters are all assumed to be completely unknown, which is different from the previous work. The design procedure includes two steps. First, according to the given periodic desired reference output and the allowed bound of tracking error, a suitable finite Fourier series expansion (FSE) is chosen as a practical reference output to be tracked. Second, by expressing the delayed practical reference output as a known time-varying vector multiplied by an unknown constant vector, we combine three kinds of uncertainties into an unknown constant vector and then estimate the vector by designing an adaptive law. By constructing a Lyapunov-Krasovskii functional, it is proved that the system output can asymptotically track the practical reference signal. An example is provided to illustrate the effectiveness of the control scheme developed in this paper.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
S. Liuzzo, R. Marino, P. Tomei. Adaptive Learning Control of Linear Systems by Output Error Feedback. Automatica, vol. 43, no. 4, pp. 669–676, 2007.
K. L. Moor. Iterative Learning Control for Deterministic System, Springer-Verlag, London, UK, 1993.
S. S. Saab. On a Discrete-time Stochastic Learning Control Algorithm. IEEE Transactions on Automatic Control, vol. 46, no. 8, pp. 1333–1336, 2001.
H. F. Chen, H. T. Fang. Output Tracking for Nonlinear Stochastic Systems by Iterative Learning Control. IEEE Transactions on Automatic Control, vol. 49, no. 4, pp. 583–588, 2004.
D. H. Owens. Universal Iterative Learning Control Using Adaptive High Gain Feedback. International Journal of Adaptive Control and Signal Processing, vol. 7, no. 5, pp. 383–388, 1993.
T. Y. Kuc, W. G. Han. Adaptive PID Learning Control of Robot Manipulators. Automatica, vol. 36, no. 5 pp. 717–725, 2000.
B. H. Park, T. Y. Kuc, J. S. Lee. Adaptive Learning Control of Uncertain Robotic Systems. International Journal of Control, vol. 65, no. 5, pp. 725–744, 1996.
W. G. Seo, B. H. Park, J. S. Lee. Intelligent Learning Control for a Class of Nonlinear Dynamic Systems. IET Proceedings: Control Theory and Applications, vol. 146, no. 2, pp. 165–170, 1999.
J. Y. Choi, J. S. Lee. Adaptive Iterative Learning Control of Uncertain Robotic Systems. IET Proceedings: Control Theory and Applications, vol. 147, no. 2, pp. 217–223, 2000.
M. French, E. Rogers. Non-linear Iterative Learning by an Adaptive Lyapunov Technique. International Journal of Control, vol. 73, no. 10, pp. 840–850, 2000.
A. Tayebi. Adaptive Iterative Learning Control for Robot Manipulators. Automatica, vol. 40, no. 7 pp. 1195–1203, 2004.
Y. C. Wang, C. J. Chien, C. C. Teng. Direct Adaptive Iterative Learning Control of Nonlinear Systems Using an Output-recurrent Fuzzy Neural Network. IEEE Transactions on Systems, Man, and Cybernetics — Part B: Cybernetics, vol. 34, no. 3, pp. 1348–1359, 2004.
J. X. Xu, B. Viswanathan. Adaptive Robust Iterative Learning Control with Dead Zone Scheme. Automatica, vol. 36, no. 1, pp. 91–99, 2000.
J. X. Xu, Y. Tian. A Composite Energy Function-based Learning Control Approach for Nonlinear Systems with Time-varying Parametric Uncertainties. IEEE Transactions on Automatic Control, vol. 47, no. 11, pp. 1940–1945, 2002.
J. X. Xu, J. Xu. On Iterative Learning from Different Tracking Tasks in the Presence of Time-varying Uncertainties. IEEE Transactions on Systems, Man, and Cybernetics — Part B: Cybernetics, vol. 34, no. 1, pp. 589–597, 2004.
S. Hara, Y. Yamamoto, T. Omata, M. Nakano. Repetitive Control System: A New Type Servo System for Periodic Exogenous Signals. IEEE Transactions on Automatic Control, vol. 33, no. 7, pp. 659–668, 1988.
X. D. Li, T. W. S. Chow, J. K. L. Ho, H. Z. Tan. Repetitive Learning Control of Nonlinear Continuous-time Systems Using Quasi-sliding Mode. IEEE Transactions on Control Systems Technology, vol. 15, no. 2, pp. 369–374, 2007.
W. E. Dixon, E. Zergeroglu, D. M. Dawson, B. T. Costic. Repetitive Learning Control: A Lyapunov-based Approach. IEEE Transactions on Systems, Man, and Cybernetics — Part B: Cybernetics, vol. 32, no. 4, pp. 538–545, 2002.
M. Sun, S. S. Ge, I. M. Y. Mareels. Adaptive Repetitive Learning Control of Robotic Manipulators without the Requirement for Initial Repositioning. IEEE Transactions on Robotics, vol. 22, no. 3, pp. 563–568, 2006.
J. X. Xu, R. Yan. On Repetitive Learning Control for Periodic Tracking Tasks. IEEE Transactions on Automatic Control, vol. 51, no. 11, pp. 1842–1848, 2006.
J. X. Xu, J. Xu. Observer Based Learning Control for a Class of Nonlinear Systems with Time-varying Parametric Uncertainties. IEEE Transactions on Automatic Control, vol. 49, no, 2, pp. 275–281, 2004.
R. W. Longman. Iterative Learning Control and Repetitive Control for Engineering Practice. International Journal of Control, vol. 73, no. 10, pp. 930–954, 2000.
S. Liuzzo, R. Marino, P. Tomei. Adaptive Learning Control of Nonlinear Systems by Output Error Feedback. IEEE Transactions on Automatic Control, vol. 52, no. 7, pp. 1232–1248, 2007.
Y. Chen, Z. Gong, C. Wen. Analysis of a High-order Iterative Learning Control Algorithm for Uncertain Nonlinear Systems with State Delays. Automatica, vol. 34, no. 3, pp. 345–353, 1998.
K. H. Park, Z. Bien, D. H. Hwang. Design of an Iterative Learning Controller for a Class of Linear Dynamic Systems with Time Delay. IET Proceedings: Control Theory and Applications, vol. 145, no. 6, pp. 507–512, 1998.
X. D. Li, T. W. S. Chow, J. K. L. Ho. 2-D System Theory Based Iterative Learning Control for Linear Continuous Systems with Time Delays. IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 52, no. 7, pp. 1421–1430, 2005.
H. Wu. Design of Iterative Learning Controllers for Linear Discrete Systems with Multiple Time Delays. IEEE Transactions on Electronics, Information and Systems, vol. 126, no. 9, pp. 1138–1143, 2006.
W. S. Chen, Y. L. Wang, J. M. Li. Adaptive Learning Control for Nonlinearly Parameterized Systems with Periodically Time-varying Delays. Acta Automatica Sinica, vol. 34, no. 12, pp. 1556–1560, 2008. (in Chinese)
M. Krstic, I. Kanellakopoulos, P. V. Kokotovic. Nonlinear Design of Adaptive Controllers for Linear Systems. IEEE Transactions on Automatic Control, vol. 39, no. 4, pp. 738–752, 1994.
X. Ye, J. Jiang. Adaptive Nonlinear Design without a Priori Knowledge of Control Directions. IEEE Transactions on Automatic Control, vol. 43, no. 11, pp. 1617–1621, 1998.
X. Ye. Adaptive Nonlinear Output-feedback Control with Unknown High-frequency Gain Sign. IEEE Transactions on Automatic Control, vol. 46, no. 1, pp. 112–115, 2001.
M. Krstic, I. Kanellakopoulos, P. V. Kokotovic. Nonlinear and Adaptive Control Design, John Wiley & Sons, Inc., New York, USA, 1995.
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was supported by National Natural Science Foundation of China (No. 60804021).
Wei-Sheng Chen received his B. Sc. degree in the Department of Mathematics from Qufu Normal University, Qufu, PRC, in 2000, the M. Sc. degree and Ph.D. degree in the Department of Applied Mathematics from Xidian University, Xi’an, PRC, in 2004 and 2007, respectively. In 2008, he was a visiting scholar in the Automation School at Southeast University, Nanjing, PRC, and is currently an associate professor in the Department of Applied Mathematics, Xidian University.
His research interests include adaptive control, learning control, neural network control, backstepping control for uncertain nonlinear systems such as time-delay or stochastic nonlinear systems.
Rights and permissions
About this article
Cite this article
Chen, WS. Novel adaptive learning control of linear systems with completely unknown time delays. Int. J. Autom. Comput. 6, 177–185 (2009). https://doi.org/10.1007/s11633-009-0177-5
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11633-009-0177-5