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

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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. © 2002 Elsevier Science (USA).

Document Type: Research Article

DOI: http://dx.doi.org/10.0000/036012799267738

Affiliations: 1: Zentrum für Technomathematik, Fachbereich 3/Mathematik und Informatik, Universität Bremen, Bremen, 28334, Germany 2: Department of Mathematics, University of Kansas, Lawrence, Kansas, 66045 3: Departamento de Ingeniería y Ciencia de Computadores, Universidad Jaume I, Castellón, 12.080, Spain 4: Departamento de Sistemas Informáticos y Computación, Universidad Politécnica de Valencia, Valencia, 46.071, Spain

Publication date: February 1, 2002

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