Adaptive control and parameter identification
Date
2015-07-02
Authors
Rabinowitz, Basil P
Journal Title
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Abstract
The broad theory of adaptive control is introduced, with
m o t i v a t i o n for using such techniques. The two mos t popu l a r
techniques, the Model Re f er e n c e A d a ptive C o n t r o l l e r s (MRAC)
and the Self Tuning C o n t r o l l e r s (STC) are studied in more
d e t a i l .
The MRAC and the STC often lead to identical solutions.
The c on d i t i o n s for which these two techni q u e s are e q u i v a l e n t
are discussed.
P a r a m e t e r Adap t a ti o n A l go r i t h m s (PAA) are required by both
the MRA a n : the STC. For this reason the PAA is e x a m i ne d
in some det.ai . This is i n itiated by de r i v i ng an o f f - l i n e
lea; -squares PAA. This is then c o n v e r t e d into a r ec u r s i v e
on-l in e estimator. Using intuitive arguments, the various
choices of gain p a r a m e t e r as well as the v a r ia t i o n s of the
nasic form o f the a l g o r i t h m are discussed. This i n c l ud e s a
w a r n in g as to w here the p i tf a l l s of such a l g o r i t h m s may lie.
In order to examine the s t a b il i t y of these a lgorithms, the
H y p e r s t a b i l i t y theorem is introduced. This requires k n o w l e d g e
of the Popov i n e q ua l i t y and Stric t l y P o s itive Real (SPR)
functions. This is intro d u c ed initially using i n t u i t i v e
ene i g y concepts after which the r i g o r ou s m a t h e m a t i c a l
representa* ion is d e r i v e d .
The H y p e r s t a b i l i t y T h e o r e m is then used to exam i n e the
s t a b i l i t y condition for various forms of the PAA.