Methods for verified stabilizing solutions to continuous-time algebraic Riccati equations
We describe a procedure based on the Krawczyk method to compute a verified enclosure for the stabilizing solution of a continuous-time algebraic Riccati equation A∗X+XA+Q=XGX building on the work of Hashemi (2012) and adding several modifications to the Krawczyk procedure. We show that after these i...
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| Veröffentlicht in: | Journal of computational and applied mathematics 2017-03, Vol.313, p.515-535 |
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| container_title | Journal of computational and applied mathematics |
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| creator | Haqiri, Tayyebe Poloni, Federico |
| description | We describe a procedure based on the Krawczyk method to compute a verified enclosure for the stabilizing solution of a continuous-time algebraic Riccati equation A∗X+XA+Q=XGX building on the work of Hashemi (2012) and adding several modifications to the Krawczyk procedure. We show that after these improvements the Krawczyk method reaches results comparable with the current state-of-the-art algorithm (Miyajima, 2015), and surpasses it in some examples. Moreover, we introduce a new direct method for verification which has a cubic complexity in term of the dimension of X, employing a fixed-point formulation of the equation inspired by the ADI procedure. The resulting methods are tested on a number of standard benchmark examples. |
| doi_str_mv | 10.1016/j.cam.2016.09.021 |
| format | Article |
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We show that after these improvements the Krawczyk method reaches results comparable with the current state-of-the-art algorithm (Miyajima, 2015), and surpasses it in some examples. Moreover, we introduce a new direct method for verification which has a cubic complexity in term of the dimension of X, employing a fixed-point formulation of the equation inspired by the ADI procedure. 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| subjects | Algebra Algebraic Riccati equation Applications of mathematics Benchmarking Interval arithmetic Krawczyk’s method Mathematical analysis Mathematical models Riccati equation Stabilizing solution State of the art Verified computation |
| title | Methods for verified stabilizing solutions to continuous-time algebraic Riccati equations |
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