Accelerated norm-optimal iterative learning control algorithms using successive projection

摘要

This article proposes a novel technique for accelerating the convergence of the previously published norm-optimal iterative learning control (NOILC) methodology. The basis of the results is a formal proof ofan observation made by D.H. Owens, namely that the NOILC algorithm is equivalent to a successiveprojection algorithm between linear varieties in a suitable product Hilbert space. This leads to two proposedaccelerated algorithms together with well-defined convergence properties. The results show that the proposedaccelerated algorithms are capable of ensuring monotonic error norm reductions and can outperform NOILCby more rapid reductions in error norm from iteration to iteration. In particular, examples indicate that theapproach can improve the performance of NOILC for the problematic case of non-minimum phase systems.Realisation of the algorithms is discussed and numerical simulations are provided for comparative purposes andto demonstrate the numerical performance and effectiveness of the proposed methods.