Learning ability of iterative learning control system with a randomly varying trial length

Abstract

This paper investigates the learning ability of iterative learning control (ILC) system with a randomly varying trial length (RVTL). The randomness of trial length is modelled as a discrete stochastic sequence. Firstly, we study the output controllability of the control system over a finite time interval. It is shown that the control system is completely controllable if and only if the input–output coupling matrix (IOCM) is full-row rank. Secondly, we propose an intermittent learning scheme with state feedback. It is strictly proved that under appropriate constraints on the learning gain and the IOCM, the ILC system with RVTL has full learning ability if and only if the probability that the trial length is equal to the desired one is greater than zero. There must exist state feedback such that the ILC process is monotonically convergent. Meanwhile, we illustrate that the proposed convergence conditions can ensure the almost sure convergence property of system output. Finally, an example is given to illustrate the merits of the ILC system with state feedback.

Keywords:

• Iterative learning control
• learning ability
• randomly varying trial lengths
• unknown system dynamics
• state feedback

Disclosure statement

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

Data availability statement

The authors confirm that the data supporting the findings of this study are available within the article and its supplementary materials.

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant number 61803291] and the Fundamental Research Funds for the Central Universities [grant number XJS210402] and Natural Science Foundation of Shaanxi Province [grant numbers 2021JQ-709, 2020JM-577, and 2019JQ066].

Notes on contributors

Yamiao Zhang

Yamiao Zhang received her B.S. degree in applied mathematics from Shaanxi University of Technology, China, in 2007, M.S. degree in applied mathematics from Xi'an University of Science and Technology, China, in 2012 and Ph.D. degree in power engineering and engineering thermophysics from Xi'an Jiaotong University, China, in 2019. Since 2019, she is with School of Science, Xi'an University of Post and Telecommunications, China. Her current research interests involve iterative learning control, networked control systems, multi-agent systems and reinforcement learning.

Jian Liu

Jian Liu received his B.S. degree in Mathematics from Fuyang Normal University, China, in 2007, M.S. degree in Mathematics from Dong Hua University, China, in 2010 and Ph.D. degree in mathematics from Xi'an Jiaotong University, China, in 2017. Since 2017, he is with School of Mechano-electronic Engineering, Xidian University, China. His current research interests involve iterative learning control, networked control systems, multi-agent systems and reinforcement learning.

Xiaoe Ruan

Xiaoe Ruan received her B.S. and M.S. degrees in mathematics from the Shaanxi Normal University, China, in 1988 and 1995, respectively and Ph.D. degree in control science and engineering from the 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. From March 2003 to August 2004, Dr. Ruan has worked as Postdoctoral Researcher in the Department of Electrical Engineering and Computer Science, Korea Advanced Institute of Science and Technology. From September 2009 to August 2010, Professor Ruan has been a visiting scholar with the Department of Electrical and Computer Engineering, Ulsan National Institute of Science and Technology, Korea. From December 2015 to February 2016, Professor Ruan has been a visiting scholar with the Department of Mechanical Engineering at the University of Texas at Dallas. Her current research interests include iterative learning control, steady-state hierarchical optimization of large-scale industrial processes, etc.