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Robust monotonic convergent iterative learning control design: An LMI‐based method
Author(s) -
Su Lanlan
Publication year - 2021
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.5617
Subject(s) - monotonic function , iterative learning control , positive definiteness , mathematics , convergence (economics) , mathematical optimization , polynomial , linear matrix inequality , convex optimization , robustness (evolution) , norm (philosophy) , robust control , semidefinite programming , computer science , regular polygon , positive definite matrix , control system , eigenvalues and eigenvectors , control (management) , artificial intelligence , quantum mechanics , political science , physics , electrical engineering , economics , gene , law , economic growth , mathematical analysis , chemistry , engineering , biochemistry , geometry
This work investigates robust monotonic convergent iterative learning control (ILC) for uncertain linear systems in both time and frequency domains, and the ILC algorithm optimizing the convergence speed in terms of l 2 norm of error signals is derived. First, it is shown that the robust monotonic convergence of the ILC system can be established equivalently by the positive definiteness of a matrix polynomial over some set. Then, a necessary and sufficient condition in the form of sum of squares for the positive definiteness is proposed, which is amendable to the feasibility of linear matrix inequalities. Based on such a condition, the optimal ILC algorithm that maximizes the convergence speed is obtained by solving a set of convex optimization problems. Moreover, the order of the learning function can be chosen arbitrarily so that the designers have the flexibility to decide the complexity of the learning algorithm.