Solving the ARE Symbolically
1993 (English)In: Proceedings of the 32nd Conference on Decision and Control, 1993, Vol. 1, 363-368 vol.1 p.Conference paper (Refereed)
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
1993. Vol. 1, 363-368 vol.1 p.
Algebraic Riccati equations, Nonlinear matrix equations, Polynomial equation systems, Gröbner bases, Elimination, Symbolic computation, Commutative algebra, Computer algebra, Real algebraic geometry, Nonlinear equation solving
IdentifiersURN: urn:nbn:se:liu:diva-94108DOI: 10.1109/CDC.1993.325129ISBN: 0-7803-1298-8OAI: oai:DiVA.org:liu-94108DiVA: diva2:629357
32nd Conference on Decision and Control, San Antonio, TX, USA, December, 1993
FunderSwedish Research Council