Convergence characteristics of iterative learning control for discrete-time singular systems

Abstract

This paper investigates the convergence characteristics of the conventional P-type iterative learning control (ILC) scheme and exploits a gain-adaptive iterative learning control mechanism for a class of linear discrete-time singular systems. Based on the lifted vector technique, the paper reforms the discrete-time singular system as a kind of algebraic input-output transmission. For the conventional P-type ILC scheme, the asymptotical convergence in terms of the tracking-error vector is achieved and the monotonic convergence in the sense of 2-norm of the tracking-error vector is derived. Further, in order to improve the learning performance, a gain-adaptive iterative learning control (GAILC) strategy is developed, which argues the iteration-time-variable gain vector while minimising the increment of quadratic tracking-error vectors of two adjacent iterations. The existence of the optimal gain vector is explored through the optimisation criterion and the algebraic approach of the columns/ rows exchanging transformation of matrix. Then the non-conditionally strictly monotonic convergence of the GAILC is made by studying the eigenvalues of the quadratic function. Finally, the validity and the effectiveness of the P-type ILC are numerically demonstrated and the remarkable outcomes of the GAILC are illustrated.

Acknowledgements

This work was supported by the National Natural Science Foundation of China under grant number F030109-61973338.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number F030109-61973338].

Notes on contributors

Ijaz Hussain

Ijaz Hussain received the M.Sc degree in mathematics from Abdul Wali Khan University, Pakistan in 2011. Currently, he is a Ph.D. candidate of Xi'an Jiaotong University, China. His research interests include iterative learning control and optimisation.

Xiaoe Ruan

Xiaoe Ruan received B.S. and M.S. degrees in mathematics from Shaanxi Normal University, China, in 1988 and 1995, respectively and Ph.D. degree in control science and engineering from Institute of Systems Science, Xi'an Jiaotong University in 2002. Since 1995, she has been with the Department of Applied Mathematics, School of Mathematics and Statistics, Xi'an Jiaotong University, China. During March 2003-August 2004, Dr. Xiaoe Ruan had worked as a post-doctoral researcher in Department of Electrical Engineering and Computer Science, Korea Advanced Institute of Science and Technology. From September 2009 to August 2010, Prof, Ruan had worked as a visiting scholar in Department of Electrical and Computer Engineering, Ulsan National Institute of Science and Technology, Korea. From December 2015 to February 2016, Professor Ruan was a visiting scholar with the Department of Mechanical Engineering at the University of Texas at Dallas. Her current research fields involve steady state hierarchical optimisation of large-scale industrial processes, iterative learning control and optimal control, etc.

Yan Liu

Yan Liu received the B.S. degree in mechanical engineering from Ningxia University, China in 2000, and the M.S. degree in electronic engineering from Xi'an Jiaotong University in 2012. Currently, she is a Ph.D. candidate of Xi'an Jiaotong University, China. Her research interests include iterative learning control and optimisation.