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Computational Experience with a Modified Newton Solver for Continuous-Time Algebraic Riccati Equations

  • Vasile SimaEmail author
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 325)

Abstract

Improved Newton solvers, with or without line search, for continuous-time algebraic Riccati equations are discussed. The basic theory and algorithms are briefly presented. Algorithmic details, the computational steps, and convergence tests are described. The main results of an extensive performance investigation of the Newton solvers are compared with those obtained using the widely-used MATLAB solver, care. Randomly generated systems with orders till 2,000, as well as the systems from the large COMPl\(_e\)ib collection of examples, are considered. Significantly improved accuracy, in terms of normalized and relative residuals, and often greater efficiency than for care have been obtained. The results strongly recommend the use of such algorithms, especially for improving the solutions computed by other solvers.

Keywords

Algebraic Riccati equation Numerical methods Optimal control Optimal estimation 

Notes

Acknowledgments

Part of this work was done in a research stay at the Technical University (TU) Chemnitz, Germany, during November 1–December 20, 2005, with financial support from the German Science Foundation. The cooperation with Peter Benner from TU Chemnitz and Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany, is much acknowledged. Thanks are also addressed to Martin Slowik from Institut für Mathematik, TU Berlin, who worked out (till 2005) a preliminary version of the SLICOT codes for CAREs. The work has been recently resumed by the author. Finally, the continuing support from the NICONET e.V. is warmly acknowledged.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.National Institute for Research and Development in InformaticsBucharestRomania

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