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

作者：Xu Guangwei; Shao Cheng; Han Yu; Yim Kangbin^*

来源：Journal of Supercomputing, 2014, 67(3): 653-670.

DOI：10.1007/s11227-013-0960-5

• Iterative learning control
• Rank-one update
• Nonlinear systems
• Quasi-Newton method

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.

• 出版日期2014-3
• 单位大连理工大学