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A generalized structured doubling algorithm for optimal control problems

Please always quote using this URN:urn:nbn:de:0296-matheon-7435
  • We propose a generalization of the Structured Doubling Algorithm (SDA) 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 (due to 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 SDA algorithm as well as some recent structured QR-methods.

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Metadaten
Author:Volker Mehrmann, Federico Poloni
URN:urn:nbn:de:0296-matheon-7435
Referee:Peter Deuflhard
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2010/12/26
Release Date:2010/12/25
Tag:
MSC-Classification:49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Jxx Existence theories / 49J15 Optimal control problems involving ordinary differential equations
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Nxx Miscellaneous topics / 49N10 Linear-quadratic problems
65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F15 Eigenvalues, eigenvectors
65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F30 Other matrix algorithms
Preprint Number:750
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