Methods for verified stabilizing solutions to continuous-time algebraic Riccati equations

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• 作者：Tayyebe Haqiri^a ; ^b ; ^{Haqiri@math.uk.ac.ir" class="auth_mail" title="E-mail the corresponding author} ; ^{thaqiri@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Federico Poloni^c ; ^{fpoloni@di.unipi.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：65M32 ; 35Kxx ; 65T60
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：313
• 期：Complete
• 页码：515-535
• 全文大小：643 K

文摘

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 i28" class="mathmlsrc">i28.gif&_user=111111111&_pii=S0377042716304411&_rdoc=1&_issn=03770427&md5=f2bb76490fe0a08e4919b55daf5277c4" title="Click to view the MathML source">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$X$, 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.