Open AccessApproximation‐based adaptive control of uncertain non‐linear pure‐feedback systems with full state constraints
Author(s) -
Kim Bong Su,
Yoo Sung Jin
Publication year - 2014
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2014.0254
Subject(s) - control theory (sociology) , bounded function , adaptive control , mathematics , lyapunov function , affine transformation , controller (irrigation) , tracking error , neighbourhood (mathematics) , state (computer science) , nonlinear system , mathematical optimization , computer science , control (management) , algorithm , mathematical analysis , artificial intelligence , physics , quantum mechanics , pure mathematics , agronomy , biology
This study proposes an adaptive approximation‐based control approach for non‐linear pure‐feedback systems in the presence of full state constraints. Completely non‐affine non‐linear functions are considered and assumed to be unknown. The dynamic surface design based on integral barrier Lyapunov functionals is provided to achieve both the desired tracking performance and the constraints satisfaction, in consideration of the full‐state‐constrained non‐affine non‐linearities. In this design procedure, simple sufficient conditions for choosing control gains, which can be checked off‐line, are established to guarantee the feasibility of the controller. The function approximation technique is employed to estimate unknown non‐linearities induced from the controller design procedure where the adaptive laws using the projection operator are designed to ensure the boundedness of the function approximators in the feasibility conditions. It is shown that all the signals in the closed‐loop system are uniformly ultimately bounded and the tracking error converges to an adjustable neighbourhood of the origin while all state variables always remain in the constrained state space.