Parallel algorithms for LQ optimal control of discrete-time periodic linear systems

Authors:
Peter Benner;Ralph Byers;Rafael Mayo;Enrique S. Quintana-Ortí;Vicente Hernández
Affiliations:
Zentrum für Technomathematik, Fachbereich 3 / Mathematik und Informatik, Universität Bremen, 28334 Bremen, Germany;Department of Mathematics, University of Kansas, Lawrence, Kansas;Departamento de Ingeniería y Ciencia de Computadores, Universidad Jaume I, 12.080 Castellón, Spain;Departamento de Ingeniería y Ciencia de Computadores, Universidad Jaume I, 12.080 Castellón, Spain;Departamento de Sistemas Informáticos y Computación, Universidad Politécnica de Valencia, 46.071 Valencia, Spain
Venue:
Journal of Parallel and Distributed Computing
Year:
2002

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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.