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Robust learning controller design for MIMO stochastic discrete‐time systems: An H ∞ ‐based approach
Author(s) -
Meng Deyuan,
Jia Yingmin,
Du Junping,
Yu Fashan
Publication year - 2011
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.1228
Subject(s) - iterative learning control , control theory (sociology) , monotonic function , discrete time and continuous time , computer science , mimo , convergence (economics) , robust control , mathematical optimization , frequency domain , tracking error , stability (learning theory) , mathematics , control system , control (management) , channel (broadcasting) , engineering , mathematical analysis , computer network , statistics , artificial intelligence , machine learning , computer vision , electrical engineering , economics , economic growth
This paper is devoted to designing iterative learning control (ILC) for multiple‐input multiple‐output discrete‐time systems that are subject to random disturbances varying from iteration to iteration. Using the super‐vector approach to ILC, statistical expressions are presented for both expectation and variance of the tracking error, and time‐domain conditions are developed to ensure their asymptotic stability and monotonic convergence. It shows that time‐domain conditions can be tied together with an H ∞ ‐based condition in the frequency domain by considering the properties of block Toeplitz matrices. This makes it possible to apply the linear matrix inequality technique to describe the convergence conditions and to obtain formulas for the control law design. Furthermore, the H ∞ ‐based approach is shown applicable to ILC design regardless of the system relative degree, which can also be used to address issues of model uncertainty. For a class of systems with a relative degree of one, simulation tests are provided to illustrate the effectiveness of the H ∞ ‐based approach to robust ILC design. Copyright © 2011 John Wiley & Sons, Ltd.