Regular Article
Parallel Algorithms for LQ Optimal Control of Discrete-Time Periodic Linear Systems

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Abstract

This paper analyzes the performance of two parallel algorithms for solving the linear-quadratic optimal control problem arising in discrete-time periodic linear systems. The algorithms perform a sequence of orthogonal reordering transformations on formal matrix products associated with the periodic linear system and then employ the so-called matrix disk function to solve the resulting discrete-time periodic algebraic Riccati equations needed to determine the optimal periodic feedback. We parallelize these solvers using two different approaches, based on a coarse-grain and a medium-grain distribution of the computational load. The experimental results report the high performance and scalability of the parallel algorithms on a Beowulf cluster.

References (38)

  • P. Benner et al.

    Solving discrete-time, periodic Riccati equations on a cluster

  • P. Benner et al.

    SLICOT—A subroutine library in systems and control theory

  • S. Bittanti et al.

    Periodic control

  • S. Bittanti et al.

    The periodic Riccati equation

  • L.S. Blackford et al.

    ScaLAPACK Users' Guide

    (1997)
  • A. Bojanczyk et al.

    The periodic Schur decomposition algorithms and applications

  • K. Braman, R. Byers, and, R. Mathias, The multi-shift QR-algorithm Part I: Maintaining well focused shifts, and level 3...
  • K. Braman, R. Byers, and, R. Mathias, The multi-shift QR-algorithm Part II: Aggressive early deflation, SIAM J. Matr....
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    Peter Benner, Rafael Mayo, and Enrique S. Quintana-Ortı́ were partially supported by the DAAD programme “Acciones Integradas Hispano-Alemanas.” Ralph Byers was partially supported by National Science Foundation awards CCR-9732671, MRI-9977352, by the NSF EPSCoR/K*STAR program through the Center for Advanced Scientific Computing, and by the National Computational Science Alliance under DMS990005N.

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