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Computing reachable sets via barrier methods on SIMD architectures

URN to cite this document: urn:nbn:de:bvb:703-epub-1964-6

Title data

Grüne, Lars ; Jahn, Thomas U.:
Computing reachable sets via barrier methods on SIMD architectures.
Department of Mathematics, University of Bayreuth
Bayreuth , 2012 . - 20 S.

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Abstract

We consider the problem of computing reachable sets of ODE-based control systems parallely on CUDA hardware. To this end, we modify an existing algorithm based on solving optimal control problems. The idea is to simplify the optimal control problems to pure feasibility problems instead of minimizing an objective function. We show that an interior point algorithm is well suited for solving the resulting feasibility problems and leads to a sequence of linear systems of equations with identical matrix layout. If the problem is defined properly, these matrices are sparse and can be transformed into a hierarchical lower arrow form which can be solved on CUDA hardware with sparse linear algebra and Cholesky’s method. We demonstrate the performance of our new algorithm by computing the reachable sets of two test problems on a CPU implementation using several explicit and implicit Runge-Kutta methods of different order. The experiments reveal a significant speedup compared to the original optimal control algorithm.

Further data

Item Type: Preprint, postprint
Keywords: reachable set; feasibility problem; sparse linear equation system; Runge-Kutta method; CUDA; parallelization; lower arrow form
DDC Subjects: 500 Science > 510 Mathematics
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne)
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-1964-6
Date Deposited: 27 Mar 2015 10:11
Last Modified: 28 Mar 2019 11:53
URI: https://epub.uni-bayreuth.de/id/eprint/1964

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