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Russia Yekaterinburg
Section  Mathematics 
Title  A parallel algorithm for constructing approximate attainable sets of nonlinear control systems 
Author(s)  Zimovets A.A.^{a}, Matviichuk A.R.^{a} 
Affiliations  Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences^{a} 
Abstract  The paper investigates the effectiveness of shared memory parallel programming approach for constructing approximate attainable sets of nonlinear control systems in a finitedimensional Euclidean space. In this study, we propose a parallel iterative algorithm for constructing approximate attainable sets employing a regular Cartesian grid for spatial discretization. The proposed algorithm has been designed for implementation on SMP systems and handles such issues as data decomposition, threads synchronization and distribution of work between multiple threads. Numerical experiments on a system with two quadcore processors confirmed a high efficiency of shared memory parallel programming approach for applying gridbased methods to construct approximate attainable sets. 
Keywords  attainability set, parallel algorithm, control system, gridbased method 
UDC  517.977.58 
MSC  93B40 
DOI  10.20537/vm150403 
Received  16 October 2015 
Language  Russian 
Citation  Zimovets A.A., Matviichuk A.R. A parallel algorithm for constructing approximate attainable sets of nonlinear control systems, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2015, vol. 25, issue 4, pp. 459472. 
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