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Nonlinear control for uncertain nonlinear systems with unknown control directions using less or no parameter estimates
Author(s) -
Zhang Zhengqiang,
Shen Hao,
Zhou Shigui,
Ma Jianping
Publication year - 2015
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.2505
Subject(s) - backstepping , control theory (sociology) , nonlinear system , parametric statistics , convergence (economics) , scheme (mathematics) , nonlinear control , dimension (graph theory) , control (management) , computer science , adaptive control , mathematics , mathematical optimization , artificial intelligence , mathematical analysis , statistics , physics , quantum mechanics , pure mathematics , economics , economic growth
Summary For the parametric strict‐feedback nonlinear systems with unknown virtual control coefficients and unknown control directions, the control schemes presented in the existing literature have the disadvantage of overparametrization. In this paper, a novel systematic design procedure is developed to solve the overparametrization problem. Two nonlinear controllers are designed by combining the backstepping technique and the Nussbaum gain approach. A main advantage of the proposed controllers is that they contain less or no parameter estimates that need to be updated online. In the first scheme, the number of the estimated parameters is equal to the dimension of the controlled system. In the second scheme, no parameter estimates are required. In both of the control schemes, the boundedness of all the closed‐loop signal is guaranteed, and the asymptotic convergence of the system states is achieved. An example is provided to demonstrate the effectiveness of the proposed design approaches. Copyright © 2014 John Wiley & Sons, Ltd.