Jacobian linearisation in a geometric setting

Linearisation is a common technique in control applications, putting useful analysis and design methodologies at the disposal of the control engineer. In this paper, linearisation is studied from a differential geometric perspective. First it is pointed out that the "naive" Jacobian techni...

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Bibliographic Details
Published in42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475) Vol. 6; pp. 6084 - 6089 Vol.6
Main Authors Tyner, D.R., Lewis, A.D.
Format Conference Proceeding
LanguageEnglish
Published IEEE 2003
Subjects
Control systems
Control theory
Controllability
Design engineering
Design methodology
Jacobian matrices
Mathematics
Optimal control
Statistical analysis
System testing
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Summary:Linearisation is a common technique in control applications, putting useful analysis and design methodologies at the disposal of the control engineer. In this paper, linearisation is studied from a differential geometric perspective. First it is pointed out that the "naive" Jacobian techniques do not make geometric sense along nontrivial reference trajectories, in that they are dependent on a choice of coordinates. A coordinate-invariant setting for linearisation is presented to address this matter. The setting here is somewhat more complicated than that seen in the naive setting. The controllability of the geometric linearisation is characterised by giving an alternate version of the usual controllability test for time-varying linear systems. The problems of stability, stabilisation, and quadratic optimal control are discussed as topics for future work.
ISBN:9780780379244
0780379241
ISSN:0191-2216
DOI:10.1109/CDC.2003.1272230