Parallel Algorithms for LQ Optimal Control of Discrete-Time Periodic Linear Systems |
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Affiliation: | 1. Laboratoire de recherche 19SP02, hôpital Abderrahmane Mami, Ariana, Tunisie;2. Faculté de médecine, université de Tunis El Manar, Tunisie, hôpital Abderrahmane Mami, Pavillon B, 2080 Ariana, Tunisie;1. C. Mateo is with the Institute for Research in Technology, School of Engineering (ICAI), Universidad Pontificia Comillas, Madrid, Spain;2. Juan A. Talavera is with ESDRAS A., S.L., Las Rozas de Madrid, Spain |
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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. |
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