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Tracking control of nonlinear systems with improved performance via transformational approach
Author(s) -
Zhao Kai,
Song Yongduan,
Chen Liang
Publication year - 2019
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.4460
Subject(s) - control theory (sociology) , overshoot (microwave communication) , tracking error , initialization , transformation (genetics) , nonlinear system , computer science , convergence (economics) , exponential stability , adaptive control , mathematics , control (management) , artificial intelligence , telecommunications , biochemistry , chemistry , physics , quantum mechanics , economics , gene , programming language , economic growth
Summary In this work, we present a transformation‐based adaptive control design, for uncertain strict‐feedback nonlinear systems, to achieve given performance specifications in terms of convergence rate/time, overshoot, steady‐state (zero‐error) precision, in addition to the primary stability requirement. For the case with no uncertainty and known control coefficient, by introducing a time‐varying scaling function and an error‐dependent transformation, we develop a control strategy that is able to achieve exponential and uniform convergence of the tracking error and at the same time maintain the output tracking overshoot to be as small as desired without the need for trajectory initialization resetting. For the case with nonparametric uncertainties and unknown control directions, by employing an additional time‐varying scaling function together with a self‐tuning Nussbaum function, we develop a control scheme that not only secures asymptotic tracking but also guarantees finite time transient process in that the tracking error, prior to converging to zero, is regulated into a prespecified residual set within a prescribed time. Both theoretical analysis and numerical simulations verify the effectiveness and benefits of the proposed method.