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Quasi-Newton-type optimized iterative learning control for discrete linear time invariant systems

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Abstract

In this paper, a quasi-Newton-type optimized iterative learning control (ILC) algorithm is investigated for a class of discrete linear time-invariant systems. The proposed learning algorithm is to update the learning gain matrix by a quasi-Newton-type matrix instead of the inversion of the plant. By means of the mathematical inductive method, the monotone convergence of the proposed algorithm is analyzed, which shows that the tracking error monotonously converges to zero after a finite number of iterations. Compared with the existing optimized ILC algorithms, due to the superlinear convergence of quasi-Newton method, the proposed learning law operates with a faster convergent rate and is robust to the ill-condition of the system model, and thus owns a wide range of applications. Numerical simulations demonstrate the validity and effectiveness.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an Shaanxi, 710049, China

    Yan Geng & Xiaoe Ruan

Authors
  1. Yan Geng
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  2. Xiaoe Ruan
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Corresponding author

Correspondence to Xiaoe Ruan.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. F010114-60974140, 61273135).

Yan GENG received the B.Sc. degree in Mathematics from Changzhi University, China in 2009. She received the M.Sc. degree in Mathematics from Hebei University, China, in 2012. Currently, she is a Ph.D. candidate of Xi’an Jiaotong University, China. Her research interests are iterative learning control and optimization.

Xiaoe RUAN received the B.Sc. and M.Sc. degrees in Pure Mathematics Education from Shaanxi Normal University, China, in 1988 and 1995, respectively. She received the Ph.D. degree in Control Science and Engineering from Xi’an Jiaotong University, China, in 2002. From March 2003 to August 2004, she worked as a postdoctoral fellow at the Department of Electrical Engineering, Korea Advance Institute of Science and Technology, Korea. From September 2009 to August 2010, she worked as a visiting scholar at Ulsan National Institute of Science and Technology, Korea. Since 1995, she joined in Xi’an Jiaotong University. Currently, she is a full professor in School of Mathematics and Statistics. She has published more than 40 academic papers. Her research interests include iterative learning control and optimized control for large-scale systems.

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Geng, Y., Ruan, X. Quasi-Newton-type optimized iterative learning control for discrete linear time invariant systems. Control Theory Technol. 13, 256–265 (2015). https://doi.org/10.1007/s11768-015-4161-z

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  • DOI: https://doi.org/10.1007/s11768-015-4161-z

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