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Adaptive tracking for MIMO nonlinear systems with Unknown fast time‐varying parameters
Author(s) -
Wu Zhongle,
Chen Jian,
Wu Chengshuai,
Zhang Kaixiang
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.4121
Subject(s) - control theory (sociology) , nonlinear system , parametric statistics , observer (physics) , parameterized complexity , convergence (economics) , singularity , controller (irrigation) , mimo , tracking (education) , computer science , lyapunov stability , backstepping , adaptive control , mathematics , stability (learning theory) , control (management) , algorithm , artificial intelligence , pedagogy , channel (broadcasting) , economic growth , mathematical analysis , computer network , biology , psychology , quantum mechanics , machine learning , agronomy , statistics , physics , economics
Summary In this paper, we consider a class of MIMO nonlinear systems with fast time‐varying parametric uncertainties. First, the tracking problem of general nonlinearly time‐varyingly parameterized systems is solved. Then, a Lyapunov‐based singularity free adaptive controller is proposed for the considered system. Specifically, an estimation approach with a proportional plus integral adaptation scheme is utilized to update the estimations of the unknown parameters under a mild assumption that the signs of the leading minors of the input gain matrix are known. The asymptotic stability is achieved with full state feedback. Furthermore, we design an output feedback controller by utilizing a standard high‐gain observer and achieve uniformly ultimately bounded convergence. Simulation examples illustrate the effectiveness of the proposed methods.