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Adaptive asymptotic stabilization of switched parametric strict‐feedback systems with switched control
Author(s) -
Zhai Ding,
An Liwei,
Zhang QingLing
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.4089
Subject(s) - backstepping , control theory (sociology) , parametric statistics , lyapunov function , adaptive control , controller (irrigation) , nonlinear system , strict feedback form , piecewise , state (computer science) , function (biology) , mathematics , class (philosophy) , exponential stability , computer science , control (management) , algorithm , mathematical analysis , statistics , physics , quantum mechanics , artificial intelligence , evolutionary biology , agronomy , biology
Summary This paper is concerned with the problem of adaptive stabilization for a class of switched linear‐parametric nonlinear systems under arbitrary switching. The traditional adaptive backstepping control is successfully extended to switched systems from nonswitched ones where the asymptotic regulation of system state is not destroyed due to rapid or abrupt changes of switching parameters. A new switched adaptive controller is designed by exploiting a common high‐order Lyapunov function with a σ ‐modification mechanism, which can reflect sufficiently the changes of plant by designing different adaptive laws and control laws for different subsystems. An explicit formula for constructing a continuous and piecewise C n − 1virtual control function is given to remove the restriction where some C ∞ bound functions have to be constructed blindly by designers in the existing results, which may be somewhat too strict to be applied. A numerical example is provided to validate the proposed approach.