Open AccessMean‐square error constrained approach to robust stochastic iterative learning control
Author(s) -
Li Li,
Liu Yang,
Yang Zhile,
Yang Xiaofeng,
Li Kang
Publication year - 2018
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2017.0546
Subject(s) - iterative learning control , minimum mean square error , control theory (sociology) , tracking error , mean squared error , convergence (economics) , mathematics , monotonic function , kalman filter , noise (video) , trace (psycholinguistics) , computer science , matrix (chemical analysis) , mathematical optimization , robust control , algorithm , control system , control (management) , artificial intelligence , statistics , mathematical analysis , linguistics , philosophy , materials science , composite material , estimator , economics , image (mathematics) , economic growth , engineering , electrical engineering
A Kalman filtering‐based robust iterative learning control algorithm is proposed in this study for linear stochastic systems with uncertain dynamics and unknown noise statistics. Firstly, a learning gain matrix is designed for the nominal case by minimising the trace of the mean‐square matrix of the input tracking error. Theoretical results show that the proposed algorithm guarantees not only the asymptotic but also monotonic convergence of the input tracking error in the mean‐square error sense, especially when random noises are Gaussian distributed the proposed algorithm is further proved to be asymptotically efficient. In addition, a new mean‐square error constrained approach is presented in designing the robust learning gain matrix, taking into account model uncertainties. A sufficient condition is provided such that the mean‐square matrix of the input tracking error is constrained within a predesigned upper bound which can monotonically converge to zero. Finally, numerical examples considering both structured and unstructured model uncertainties are included to illustrate the effectiveness of the proposed algorithms.