| 1. |
- Ljung, Stefan, et al.
(författare)
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Error Propagation Properties of Recursive Least-Squares Adaptation Algorithms
- 1984
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Ingår i: Proceedings of the 9th IFAC World Congress. - : Pergamon. - 0080316662 ; , s. 70-74
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Konferensbidrag (refereegranskat)abstract
- The numerical properties of implementations of the recursive least-squares identification algorithm are of great importance for their continuous use in various adaptive schemes. Here we investigate how an error that is introduced at an arbitrary point in the algorithm propagates. It is shown that conventional LS algorithms, including Bierman's UD-factorization algorithm are exponentially stable with respect to such errors, i.e. the effect of the error decays exponentially. The base of the decay is equal to the forgetting factor. The same is true for fast lattice algorithms. The fast least-squares algorithm, sometimes known as the ‘fast Kalman algorithm’ is however shown to be unstable with respect to such errors.
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| 2. |
- Ljung, Stefan, et al.
(författare)
-
Error Propagation Properties of Recursive Least Squares Adaptation Algorithms
- 1983
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The numerical properties of implementations of the recursive least-squares identification algorithm are of great importance for their continuous use in various adaptive schemes. Here we investigate how an error that is introduced at an arbitrary point in the algorithm propagates. It is shown that conventional LS algorithms, including Bierman's UD-factorization algorithm are exponentially stable with respect to such errors, i.e. the effect of the error decays exponentially. The base of the decay is equal to the forgetting factor. The same is true for fast lattice algorithms. The fast least-squares algorithm, sometimes known as the ‘fast Kalman algorithm’ is however shown to be unstable with respect to such errors.
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| 3. |
- Ljung, Stefan, et al.
(författare)
-
Fast Numerical Solution of Fredholm Integral Equations with Stationary Kernels
- 1980
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A fast recursive matrix method for the numerical solution of Fredholm integral equations with stationary kernels is derived. IfN denotes the number of nodal points, the complexity of the algorithm isO(N 2), which should be compared toO(N 3) for conventional algorithms for solving such problems. The method is related to fast algorithms for inverting Toeplitz matrices.Applications to equations of the first and second kind as well as miscellaneous problems are discussed and illustrated with numerical examples. These show that the theoretical improvement in efficiency is indeed obtained, and that no problems with numerical stability or accuracy are encountered.
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| 4. |
- Ljung, Stefan, et al.
(författare)
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Fast Numerical Solution of Fredholm Integral Equations with Stationary Kernels
- 1982
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Ingår i: BIT Numerical Mathematics. - : Kluwer Academic Publishers. - 0006-3835 .- 1572-9125. ; 22:1, s. 54-72
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Tidskriftsartikel (refereegranskat)abstract
- A fast recursive matrix method for the numerical solution of Fredholm integral equations with stationary kernels is derived. IfN denotes the number of nodal points, the complexity of the algorithm isO(N 2), which should be compared toO(N 3) for conventional algorithms for solving such problems. The method is related to fast algorithms for inverting Toeplitz matrices.Applications to equations of the first and second kind as well as miscellaneous problems are discussed and illustrated with numerical examples. These show that the theoretical improvement in efficiency is indeed obtained, and that no problems with numerical stability or accuracy are encountered.
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| 5. |
- Andersson, Peter, et al.
(författare)
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A Test Case for Adaptive Control : Car Steering
- 1981
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Ingår i: Proceedings of the 1981 IFAC Symposium on Theory and Applications of Digital Control. - Linköping : Linköping University. - 9780080276182
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Rapport (övrigt vetenskapligt/konstnärligt)
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| 6. |
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| 7. |
- Friedlander, Benjamin, et al.
(författare)
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Lattice Implementation of the Recursive Maximum Likelihood Algorithm
- 1981
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Ingår i: Proceedings of the 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes. - Linköping : Linköping University. ; , s. 1083-1084
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A lattice implementation of the extended least-squares algorithm was recently developed. The convergence of that algorithm depends on a positive real condition, a fact which limits its usefulness in some applications. In this note the lattice equivalent of the recursive maximum likelihood algorithm is derived. This technique does not require the positive real condition and is suitable for modeling and prediction of general ARMA time-series.
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| 8. |
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| 9. |
- Glad, Torkel, 1947-, et al.
(författare)
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Reglerteknik : grundläggande teori
- 1981
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- Boken behandlar grundläggande metoder för beskrivning, analys och dimensionering av reglersystem. Klassiska angreppssätt som rotortmetoden och frekvensanalys med hjälp av Bodediagram diskuteras.Dessutom introduceras tillståndsvariabler och metoder att analysera känslighet och robusthet hos reglersystem. Grunderna för behandling av olinjära fenomen och digital implementering av regulatorer diskuteras.Bokens omfattning motsvarar en typisk grundkurs i reglerteknik inom civilingenjörsutbildningen.
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| 10. |
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