A generalized structured doubling algorithm for the numerical solution of linear quadratic optimal control problems. Issue 1 (12th March 2012)

• Record Type: Journal Article
• Authors: Mehrmann, Volker; Poloni, Federico
• Is Part Of: Numerical linear algebra with applications. Volume 20:Issue 1(2013:Jan.)
• Page Start: 112
• Page End: 137
• Publication Date: 2012-03-12
• Subjects: structured doubling algorithm -- optimal control -- symplectic pencil -- Cayley transformation -- disk function method -- pencil arithmetic; Algebras, Linear -- Periodicals; 512.5
• DOI: 10.1002/nla.1828
• Languages: English
• ISSNs: 1070-5325

Abstract

SUMMARY: We propose a generalization of the structured doubling algorithm to compute invariant subspaces of structured matrix pencils that arise in the context of solving linear quadratic optimal control problems. The new algorithm is designed to attain better accuracy when the classical Riccati equation approach for the solution of the optimal control problem is not well suited because the stable and unstable invariant subspaces are not well separated (because of eigenvalues near or on the imaginary axis) or in the case when the Riccati solution does not exist at all. We analyze the convergence of the method and compare the new method with the classical structured doubling algorithm as well as some structured QR methods. Copyright © 2012 John Wiley & Sons, Ltd.