Premium
An approach to digital implementation of continuous backstepping adaptive control for linear systems
Author(s) -
Rabeh A.,
Ikhouane F.,
Giri F.
Publication year - 1999
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/(sici)1099-1115(199908)13:5<327::aid-acs538>3.0.co;2-x
Subject(s) - backstepping , control theory (sociology) , bounded function , adaptive control , discrete time and continuous time , controller (irrigation) , tracking error , sampling (signal processing) , representation (politics) , computer science , digital control , adaptive sampling , mathematics , control (management) , engineering , filter (signal processing) , statistics , artificial intelligence , mathematical analysis , electrical engineering , politics , law , political science , agronomy , computer vision , biology , monte carlo method
This paper presents a solution to the problem of digitally implementing backstepping adaptive control for linear systems. The continuous‐time system to be controlled is given a discrete‐time representation in the δ ‐operator. A discrete adaptive backstepping controller is then designed for such a discrete‐time model. The effect of the modelling error, generated by the sampling process, is accounted for in the parameter update law by a σ ‐modification. It is shown that all the signals (discrete and continuous) of the closed loop are uniformly bounded, with a region of attraction which is a K ∞ function of the sampling rate. An upper bound on the asymptotic tracking error is then given, and shown to be proportional to the sampling period. Copyright © 1999 John Wiley & Sons, Ltd.