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Solving the ARE Symbolically
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
1993 (English)Report (Other academic)
Abstract [en]

Methods from computer algebra, mostly so called Grobner bases (gb) from commutative algebra, are used to solve the algebraic Riccati equation (ARE) symbolically. The methods suggested allow us to track the influence of parameters in the system or penalty matrices on the solution. Some nontrivial aspects arise when addressing the problem from the point of view commutative algebra, for example the original equations are rational, not polynomial. We explain how this can be dealt with rather easily. Some methods for lowering the computational complexity are suggested and different methods are compared regarding efficiency. Preprocessing of the equations before applying gb can make computations more efficient.

Place, publisher, year, edition, pages
Linköping: Linköping University , 1993. , 12 p.
Series
LiTH-ISY-R, ISSN 1400-3902 ; 1456
Keyword [en]
Algebraic Riccati equations, Nonlinear matrix equations, Polynomial equation systems, Gröbner bases, Elimination, Symbolic computation, Commutative algebra, Computer algebra, Real algebraic geometry, Nonlinear equation solving
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-55583ISRN: LiTH-ISY-R-1456OAI: oai:DiVA.org:liu-55583DiVA: diva2:316333
Funder
Swedish Research Council
Available from: 2010-04-30 Created: 2010-04-30 Last updated: 2014-09-12Bibliographically approved

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Automatic ControlThe Institute of Technology
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CiteExportLink to record
Permanent link

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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf