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Boundedness conjecture for an output error adaptive algorithm
Author(s) -
Schoenwald D. A.,
Kokotovic P. V.
Publication year - 1990
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.4480040104
Subject(s) - control theory (sociology) , bounded function , mathematics , stability (learning theory) , instability , exponential stability , signal (programming language) , transfer function , magnitude (astronomy) , function (biology) , stability theory , conjecture , computer science , nonlinear system , mathematical analysis , engineering , physics , control (management) , quantum mechanics , artificial intelligence , machine learning , astronomy , evolutionary biology , mechanics , pure mathematics , electrical engineering , biology , programming language
Abstract This paper compares conditions for instability with conditions for global asymptotic stability of a discretetime output error adaptive estimation algorithm. This comparison leads to a boundedness conjecture which states that all signals within this adaptive system as well as the output error and parameter estimates remain globally bounded for all time despite any unstable behaviour. The investigation into the stability properties of this algorithm begins with a global stability criterion applied to a transfer function which is not strictly positive real. This criterion states that for large enough adaptation gain and/or input signal magnitude the system will be asymptotically stable. Then a local result is applied which states that for small enough adaptation gain and/or input signal magnitude the same system is unstable. The result is a bifurcation due to the decrease of the adaptation gain and/or input signal magnitude as the system goes from asymptotic stability to instability which remains bounded. The results suggested by the computer simulations are verified by an exact analysis of a linearized periodic version of the adaptive system.