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Stability of self‐tuning control based on Lyapunov function
Author(s) -
Patete A.,
Furuta K.,
Tomizuka M.
Publication year - 2008
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.1027
Subject(s) - control theory (sociology) , minimum phase , minimum variance unbiased estimator , controller (irrigation) , stability (learning theory) , lyapunov function , self tuning , mathematics , variance (accounting) , function (biology) , lyapunov stability , computer science , control (management) , transfer function , control engineering , engineering , pid controller , nonlinear system , statistics , mean squared error , temperature control , artificial intelligence , business , biology , accounting , quantum mechanics , machine learning , evolutionary biology , agronomy , physics , electrical engineering
The overall stability of a self‐tuning controller for discrete‐time systems is proved by using the Lyapunov function in this paper, for minimum and a class of non‐minimum phase systems. The self‐tuning controller utilizes a recursive estimate algorithm for the controller parameters based on the generalized minimum variance criterion. Previously, the stability had been proved in the case of minimum phase systems. A new type of self‐tuning controller for the discrete‐time system with delay in control input is also studied which is named the generalized minimum variance criterion‐β equivalent control, and its stability is proved. The simulation is done to evaluate the performance of the proposed self‐tuning controller. Copyright © 2008 John Wiley & Sons, Ltd.