Tracking Control Strategy Using Filter-Based Approximation for theUnknown Control Direction Problem of Uncertain Pure-Feedback Nonlinear Systems

A filter-based recursive tracker design approach is presented for the problem of unknown control directions of pure-feedback systems with completely unknown non-affine nonlinearities. In the controller design procedure, the first-order filters for error surfaces, a control input, and state variables...

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Bibliographic Details
Published inMathematics (Basel) Vol. 8; no. 8; p. 1341
Main Authors Yun Ho Choi, Sung Jin Yoo
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.01.2020
Subjects
Adaptation
Adaptive control
Adaptive filters
Approximation
Control systems design
Control theory
Controllers
Coordinate transformations
Design
Error reduction
Feedback
Fuzzy logic
Mathematical analysis
Mathematics
Neural networks
Nonlinear systems
Recursive methods
Stability analysis
State variable
Tracking control
Tracking errors
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Summary:A filter-based recursive tracker design approach is presented for the problem of unknown control directions of pure-feedback systems with completely unknown non-affine nonlinearities. In the controller design procedure, the first-order filters for error surfaces, a control input, and state variables are employed to design nonadaptive virtual and actual control laws independent of adaptive function approximators. In addition, for the unknown control direction problem, the filtering signals are incorporated with Nussbaum functions. Different from existing adaptive approximation-based control schemes in the presence of unknown control directions, the proposed approach does not require any adaptive technique regardless of completely unknown nonlinear functions. Therefore, a simplified tracking structure can be constructed. Using the Lyapunov stability analysis, it is shown that the tracking error is reduced within an adjustable neighborhood of the origin while ensuring all the closed-loop signals are bounded.
ISSN:2227-7390
DOI:10.3390/math8081341