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Robust learning control for nonlinear systems with nonparametric uncertainties and nonuniform trial lengths
Author(s) -
Shen Dong,
Xu JianXin
Publication year - 2018
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.4437
Subject(s) - bounded function , nonparametric statistics , norm (philosophy) , nonlinear system , tracking error , iterative learning control , mathematics , mathematical optimization , robust control , random variable , computer science , control theory (sociology) , convergence (economics) , control (management) , statistics , artificial intelligence , mathematical analysis , physics , quantum mechanics , political science , law , economics , economic growth
Summary This paper proposes robust iterative learning control schemes for continuous‐time nonlinear systems with various nonparametric uncertainties under nonuniform trial length circumstances. The nonuniform trial length is described by a random variable, which causes a random data missing problem while designing and analyzing algorithms for the precise tracking problem. Three common types of nonparametric uncertainties are taken into account: norm‐bounded uncertainty, variation‐norm‐bounded uncertainty, and norm‐bounded uncertainty with unknown coefficients. A novel composite energy function is introduced with the help of a newly defined virtual tracking error for the asymptotical convergence of the proposed schemes. Extensions to multiple‐input–multiple‐output cases are also elaborated. Illustrative simulations are provided to verify the theoretical results.