NDLI: Output regulation for infinite-dimensional linear systems periodic reference signals from Sobolev spaces

Content Provider	IEEE Xplore Digital Library
Author	Immonen, E. Pohjolainen, S.
Copyright Year	2004
Description	Author affiliation: Inst. of Math., Tampere Univ. of Technol., Finland (Immonen, E.; Pohjolainen, S.)
Abstract	We study asymptotic tracking and rejection (i.e. regulation) of continuous periodic signals in the context of exponentially stabilizable linear infinite-dimensional systems. Our reference signals are in Sobolev type spaces H(/spl omega//sub n/, f/sub n/) and they (as well as the disturbance signals) are generated by an infinite-dimensional exogenous system. We show that there exists a feedforward controller which achieves output regulation if and only if the so called regulator equations are satisfied and a decomposability condition holds. We show that if the stabilized plant does not have transmission zeros at the frequencies i/spl omega//sub n/ of the reference signals, then all reference signals in H(/spl omega//sub n/, f/sub n/) can be asymptotically tracked in the presence of disturbances if and only if (H/sub K/(i/spl omega//sub n/)/sup -1/[1-H/sub d/(i/spl omega//sub n/)/spl phi//sub n/]fn/sup -1/)/sub n/spl epsiv/I/ /spl epsiv//spl lscr/ /sup 2/. Here H/sub K/(i/spl omega//sub n/) and H/sub d/(i/spl omega//sub n/) are certain transfer functions evaluated at points i/spl omega//sub n/ and the sequence (f/sub n/) consists of weights for the Fourier coefficients of the reference signals. Three examples are given to illustrate the theory.
Starting Page	2859
Ending Page	2864
File Size	169796
Page Count	6
File Format	PDF
ISBN	0780386825
ISSN	01912216
DOI	10.1109/CDC.2004.1428898
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2004-12-14
Publisher Place	Bahamas
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Linear systems Signal generators Robust control Control systems Regulators Equations Frequency Transfer functions Adaptive control Mathematics
Content Type	Text
Resource Type	Article

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