Abstract
In this paper, we use the iterative learning control algorithm to deal with generalized distributed parameter system with parabolic type which described by generalized partial differential equation. Because of the particularity of the generalized system, we usually need generalized value decomposition, but the algorithm we proposed in this paper does not need to consider the impulsive solution of the generalized system, so it can simplify the calculation process. A novel generalized theoretical result is presented by using the PD-type learning law under some assumptions. The convergence conditions of algorithm are established. By the basic generalized theory, matrix theory and mapping principle, the paper gives rigorous convergence proof of the algorithm to ensure the tracking error is convergent in L2 norm. Finally, we use an example to verify the validity of the new proposed algorithm. Through this paper, we can do further study and discuss the iterative learning algorithm for generalized distributer parameter system in the future.
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Acknowledgments
The work was supported by the Hechi University Foundation (XJ2016ZD004), Hechi University Youth teacher Foundation (XJ2017QN08), the Projection of Environment Master Foundation (2017HJA001, 2017HJB001), the important Project of the New Century Teaching Reform Project in Guangxi (2010JGZ033) and Guangxi Youth teacher Foundation (2018KY0495).
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All authors contributed equally and significantly in writing this article. All authors read and approved the final manuscript. Yinghui Li is the corresponding author.
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Zhang, Y., Li, Y. & Chen, M. Iterative learning control for linear generalized distributed parameter system. Neural Comput & Applic 31, 4503–4512 (2019). https://doi.org/10.1007/s00521-018-3835-0
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DOI: https://doi.org/10.1007/s00521-018-3835-0