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

  • Authors:

  • Guangwei Xu;Cheng Shao;Yu Han;Kangbin Yim

  • Affiliations:

  • Institute of Advanced Control Technology, Dalian University of Technology, Dalian, China 116024;Institute of Advanced Control Technology, Dalian University of Technology, Dalian, China 116024;School of Software, Dalian University of Technology, Dalian, China 116024;Dept. of Information Security Engineering, Soonchunhyang University, Asan, South Korea 336-745

  • Venue:
  • The Journal of Supercomputing
  • Year:
  • 2014

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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.