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Multivariable Adaptive Control

Johansson, Rolf LU (1983) In PhD Thesis TFRT-1024
Abstract
This thesis treats the problem of direct adaptive control of linear multivariable systems. The parametrization problem of adaptive control is discussed extensively. A pole-placement problem and a model-matching problem are formulated and interpreted in terms of model reference control. The problem is solved via a discussion on system invariants of multivariable systems as presented by Pernebo. The attention is then directed towards problems of identification and two different estimation schemes are formulated. Parameter convergence is guaranteed provided some conditions on /a priori/ information are satisfied. The requested prior knowledge is formulated in terms of the non-invertible system for the suggested prediction error... (More)
This thesis treats the problem of direct adaptive control of linear multivariable systems. The parametrization problem of adaptive control is discussed extensively. A pole-placement problem and a model-matching problem are formulated and interpreted in terms of model reference control. The problem is solved via a discussion on system invariants of multivariable systems as presented by Pernebo. The attention is then directed towards problems of identification and two different estimation schemes are formulated. Parameter convergence is guaranteed provided some conditions on /a priori/ information are satisfied. The requested prior knowledge is formulated in terms of the non-invertible system for the suggested prediction error identification algorithm. The second parameter adjustment law is shown to converge when a certain approximant of the left structure matrix, /i.e./, the system invariant is known. This result relaxes a result by Elliott /et al./ where the interactor is required to be known.

The important question of stability of adaptive systems is also treated. The major result is a method for construction of Lyapunov functions for a class of single-input systems. Stability in the sense of Lyapunov and exponential convergence are shown.

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supervisor
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publishing date
type
Thesis
publication status
published
subject
in
PhD Thesis TFRT-1024
publisher
Department of Automatic Control, Lund Institute of Technology (LTH)
ISSN
0280-5316
0280-5316
language
English
LU publication?
yes
id
b77e60bc-3352-46e0-bc70-2021537ac85a (old id 8524853)
date added to LUP
2016-04-01 16:35:50
date last changed
2019-05-23 15:31:34
@phdthesis{b77e60bc-3352-46e0-bc70-2021537ac85a,
  abstract     = {This thesis treats the problem of direct adaptive control of linear multivariable systems. The parametrization problem of adaptive control is discussed extensively. A pole-placement problem and a model-matching problem are formulated and interpreted in terms of model reference control. The problem is solved via a discussion on system invariants of multivariable systems as presented by Pernebo. The attention is then directed towards problems of identification and two different estimation schemes are formulated. Parameter convergence is guaranteed provided some conditions on /a priori/ information are satisfied. The requested prior knowledge is  formulated in terms of the non-invertible system for the suggested prediction error identification algorithm. The second parameter adjustment law is shown to converge when a certain approximant of the left structure matrix, /i.e./, the system invariant is known. This result relaxes a result by Elliott /et al./ where the interactor is required to be known.<br/><br/>The important question of stability of adaptive systems is also treated. The major result is a method for construction of Lyapunov functions for a class of single-input systems. Stability in the sense of Lyapunov and exponential convergence are shown.<br/><br/>},
  author       = {Johansson, Rolf},
  issn         = {0280-5316},
  language     = {eng},
  publisher    = {Department of Automatic Control, Lund Institute of Technology (LTH)},
  school       = {Lund University},
  series       = {PhD Thesis TFRT-1024},
  title        = {Multivariable Adaptive Control},
  url          = {https://lup.lub.lu.se/search/ws/files/4719569/8569292.pdf},
  year         = {1983},
}