- -

Solving time-invariant differential matrix Riccati equations using GPGPU computing

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

Solving time-invariant differential matrix Riccati equations using GPGPU computing

Mostrar el registro sencillo del ítem

Ficheros en el ítem

[Cerrado]
Nombre: Peinado;Alonso;Ibáñez ...
Tamaño: 276.9Kb
Formato: PDF
Descripción: Versión editorial
Solicitar una copia al autor
dc.contributor.author Peinado Pinilla, Jesús es_ES
dc.contributor.author Alonso-Jordá, Pedro es_ES
dc.contributor.author Ibáñez González, Jacinto Javier es_ES
dc.contributor.author Hernández García, Vicente es_ES
dc.contributor.author DO CARMO BORATTO, MURILO es_ES
dc.date.accessioned 2015-04-24T08:10:28Z
dc.date.available 2015-04-24T08:10:28Z
dc.date.issued 2014-11
dc.identifier.issn 0920-8542
dc.identifier.uri http://hdl.handle.net/10251/49225
dc.description.abstract Differential matrix Riccati equations (DMREs) enable to model many physical systems appearing in different branches of science, in some cases, involving very large problem sizes. In this paper, we propose an adaptive algorithm for time-invariant DMREs that uses a piecewise-linearized approach based on the Padé approximation of the matrix exponential. The algorithm designed is based upon intensive use of matrix products and linear system solutions so we can seize the large computational capability that modern graphics processing units (GPUs) have on these types of operations using CUBLAS and CULATOOLS libraries (general purpose GPU), which are efficient implementations of BLAS and LAPACK libraries, respectively, for NVIDIA © GPUs. A thorough analysis showed that some parts of the algorithm proposed can be carried out in parallel, thus allowing to leverage the two GPUs available in many current compute nodes. Besides, our algorithm can be used by any interested researcher through a friendly MATLAB © interface. es_ES
dc.language Inglés es_ES
dc.publisher Springer Verlag (Germany) es_ES
dc.relation.ispartof Journal of Supercomputing es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Differential matrix Riccati equation (DMRE) es_ES
dc.subject Ordinary differential equation (ODE) es_ES
dc.subject Piecewise-linearized method es_ES
dc.subject Padé approximants es_ES
dc.subject GPGPU es_ES
dc.subject.classification CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL es_ES
dc.subject.classification LENGUAJES Y SISTEMAS INFORMATICOS es_ES
dc.title Solving time-invariant differential matrix Riccati equations using GPGPU computing es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s11227-014-1111-3
dc.rights.accessRights Cerrado es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Sistemas Informáticos y Computación - Departament de Sistemes Informàtics i Computació es_ES
dc.contributor.affiliation Universitat Politècnica de València. Instituto de Instrumentación para Imagen Molecular - Institut d'Instrumentació per a Imatge Molecular es_ES
dc.description.bibliographicCitation Peinado Pinilla, J.; Alonso-Jordá, P.; Ibáñez González, JJ.; Hernández García, V.; Do Carmo Boratto, M. (2014). Solving time-invariant differential matrix Riccati equations using GPGPU computing. Journal of Supercomputing. 70(2):623-636. doi:10.1007/s11227-014-1111-3 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://link.springer.com/article/10.1007%2Fs11227-014-1111-3 es_ES
dc.description.upvformatpinicio 623 es_ES
dc.description.upvformatpfin 636 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 70 es_ES
dc.description.issue 2 es_ES
dc.relation.senia 269384
dc.description.references Anderson E et al (1994) LAPACK users’ guide. SIAM, Philadelphia es_ES
dc.description.references Arias E, Hernández V, Ibáñez J, Peinado J (2007) A fixed point-based BDF method for solving Riccati equations. Appl Math Comput 188(2):1319–1333 es_ES
dc.description.references Benner P, Mena H (2004) BDF methods for large-scale differential Riccati equations. In: 16th International symposium on mathematical theory of network and systems (MTNS2004), Katholieke Universiteit Leuven, Belgium es_ES
dc.description.references Benner P, Mena H (2013) Rosenbrock methods for solving Riccati differential equations. IEEE Trans Autom Control 58(11):2950–2956 es_ES
dc.description.references Chandrasekhar H (1976) Generalized Chandrasekhar algorithms: time-varying models. IEEE Trans Autom Control 21:728–732 es_ES
dc.description.references Chen B, Company R, Jdar L, Rosell MD (2007) Constructing accurate polynomial approximations for nonlinear differential initial value problems. Appl Math Comput 193:523–534 es_ES
dc.description.references Choi CH (1988) Efficient algorithms for solving stiff matrix-valued Riccati differential equations. PhD thesis, University of California, California es_ES
dc.description.references Choi CH (1992) Time-varying Riccati differential equations with known analytic solutions. IEEE Trans Autom Control 37:642–645 es_ES
dc.description.references Davison EJ, Maki MC (1973) The numerical solution of the matrix Riccati differential equation. IEEE Trans Autom Control 18(1):71–73 es_ES
dc.description.references Defez E, Hervs A, Soler L, Tung MM (2007) Numerical solutions of matrix differential models using cubic matrix splines II. Math Comput Model 46:657–669 es_ES
dc.description.references Dieci L (1992) Numerical integration of the differential Riccati equation and some related issues. SIAM J Numer Anal 29(3):781–815 es_ES
dc.description.references EM Photonics (2011) CULATOOLS, R12 edn es_ES
dc.description.references Hernández V, Ibáñez J, Arias E, Peinado J (2008) A GMRES-based BDF method for solving differential Riccati equations. Appl. Math. Comput. 196(2):613–626 es_ES
dc.description.references Horn RA, Johnson CR (1991) Topics in matrix analysis. Cambridge University Press, London es_ES
dc.description.references Ibáñez J, Hernández V (2010) Solving differential matrix Riccati equations by a piecewise-linearized method based on the conmutant equation. Comput Phys Commun 180:2103–2114 es_ES
dc.description.references Ibáñez J, Hernández V (2011) Solving differential matrix Riccati equations by a piecewise-linearized method based on diagonal Padé approximants. Comput Phys Commun 182:669–678 es_ES
dc.description.references Ibáñez J, Hernández V, Arias E, Ruiz P (2009) Solving initial value problems for ordinary differential equations by two approaches: BDF and piecewise-linearized methods. Comput Phys Commun 180(5):712–723 es_ES
dc.description.references Kenney CS, Leipnik RB (1985) Numerical integration of the differential matrix Riccati equation. IEEE Trans Autom Control 30:962–970 es_ES
dc.description.references Li R-C (2000) Unconventional reflexive numerical methods for matrix differential Riccati. In: Technical report 2000-36, Department of Mathematics, University of Kentucky, Lexington es_ES
dc.description.references MathWorks (2013) MATLAB MEX files. http://www.mathworks.es/es/help/matlab/create-mex-files.html . Accessed June 2013 es_ES
dc.description.references MathWorks (2013) MATLAB parallel computing toolbox. http://www.mathworks.es/products/parallel-computing . Accessed June 2013 es_ES
dc.description.references Meyer GH (1973) Initial value methods for boundary value problems. Academic Press, New York es_ES
dc.description.references NVIDIA Corporation (2013) CUBLAS library. http://docs.nvidia.com/cuda/cublas/ . Accessed June 2013 es_ES
dc.description.references NVIDIA Corporation (2013) CUDA C programming guide.  http://docs.nvidia.com/cuda/cuda-c-programming-guide . Accessed June 2013 es_ES
dc.description.references Ramos JI, García CM (1997) Piecewise-linearized methods for initial-value problems. Appl Math Comput 82:273–302 es_ES
dc.description.references Rand DW, Winternitz P (1984) Nonlinear superposition principles: a new numerical method for solving matrix Riccati equations. Comput Phys Commun 33:305–328 es_ES
dc.description.references Sanz-Serna JM (1992) Symplectic integrators for Hamiltonian problems: an overview. Acta Numer 1:243–286 es_ES
dc.description.references Sastre J, Ibez J, Defez E, Ruiz P (2011) Accurate matrix exponential computation to solve coupled differential models in engineering. Math Comput Model 54:1835–1840 es_ES
dc.description.references Sorine M, Winternitz P (1985) Superposition laws for the solution of differential Riccati equations. IEEE Trans Autom Control 30:266–272 es_ES
dc.description.references Vaughan DR (1969) A negative exponential solution for the matrix Riccati equation. IEEE Trans Autom Control 14(1):72–75 es_ES


Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro sencillo del ítem