Abstract
The numerical treatment of the linear-quadratic optimal control problem requires the solution of Riccati equations. In particular, the differential Riccati equations (DRE) is a key operation for the computation of the optimal control in the finite-time horizon case. In this work, we focus on large-scale problems governed by partial differential equations (PDEs) where, in order to apply a feedback control strategy, it is necessary to solve a large-scale DRE resulting from a spatial semi-discretization. To tackle this problem, we introduce an efficient implementation of the implicit Euler method and linearly implicit Euler method on hybrid CPU-GPU platforms for solving differential Riccati equations arising in a finite-time horizon linear-quadratic control problems. Numerical experiments validate our approach.
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Acknowledgment
H. Mena was supported by the project Solution of large-scale Lyapunov Differential Equations (P 27926) founded by the Austrian Science Foundation FWF. E.S. Quintana was supported by the CICYT project TIN2014-53495-R of the Ministerio de Economía y Competitividad and FEDER. E. Dufrechou, P. Ezzatti and A. Remón were supported by the EHFARS project funded by the German Ministry of Education and Research BMBF.
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Benner, P., Dufrechou, E., Ezzatti, P., Mena, H., Quintana-Ortí, E.S., Remón, A. (2017). Solving Sparse Differential Riccati Equations on Hybrid CPU-GPU Platforms. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2017. ICCSA 2017. Lecture Notes in Computer Science(), vol 10404. Springer, Cham. https://doi.org/10.1007/978-3-319-62392-4_9
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