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New quasi-Newton iterative learning control scheme based on rank-one update for nonlinear systems

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Abstract

This paper develops an algorithm for iterative learning control on the basis of the quasi-Newton method for nonlinear systems. The new quasi-Newton iterative learning control scheme using the rank-one update to derive the recurrent formula has numerous benefits, which include the approximate treatment for the inverse of the system’s Jacobian matrix. The rank-one update-based ILC also has the advantage of extension for convergence domain and hence guaranteeing the choice of initial value. The algorithm is expressed as a very general norm optimization problem in a Banach space and, in principle, can be used for both continuous and discrete time systems. Furthermore, a detailed convergence analysis is given, and it guarantees theoretically that the proposed algorithm converges at a superlinear rate. Initial conditions which the algorithm requires are also established. The simulations illustrate the theoretical results.

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Authors and Affiliations

  1. Institute of Advanced Control Technology, Dalian University of Technology, 2 Linggong, Ganjingzi, Dalian, 116024, China

    Guangwei Xu & Cheng Shao

  2. School of Software, Dalian University of Technology, 2 Linggong, Ganjingzi, Dalian, 116024, China

    Yu Han

  3. Dept. of Information Security Engineering, Soonchunhyang University, 646 Eupnae, Shinchang, Asan, 336-745, South Korea

    Kangbin Yim

Authors
  1. Guangwei Xu
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  2. Cheng Shao
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  3. Yu Han
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  4. Kangbin Yim
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Correspondence to Kangbin Yim.

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Xu, G., Shao, C., Han, Y. et al. New quasi-Newton iterative learning control scheme based on rank-one update for nonlinear systems. J Supercomput 67, 653–670 (2014). https://doi.org/10.1007/s11227-013-0960-5

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  • DOI: https://doi.org/10.1007/s11227-013-0960-5

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