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Transient bounds of dynamic certainty equivalent adaptive controllers
Author(s) -
Ortega Romeo
Publication year - 1993
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.4480070406
Subject(s) - control theory (sociology) , backstepping , norm (philosophy) , estimator , transient (computer programming) , transient response , mathematics , upper and lower bounds , computer science , adaptive control , mathematical optimization , engineering , control (management) , artificial intelligence , statistics , mathematical analysis , electrical engineering , political science , law , operating system
In this paper we show that the transient bounds of Morse's dynamic certainty equivalent adaptive controller established previously by us can be considerably strengthened. Specifically, we derive a computable bound on the ℒ ∞ ‐norm of the tracking error which, in contrast with the local bound obtained previously by us, holds for all system initial conditions. Also, we add an ‘adaptation gain’ in the high‐order estimator to prove that, by increasing this gain, the ℒ ∞ ‐norm of the tracking error can be made arbitrarily small without increasing its ℒ ∞ norm. This is an improvement over the results obtained with backstepping designs, where these performance measures must be traded off in the selection of the adaptation speed.