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dc.contributor.author | Bader, Philipp | es_ES |
dc.contributor.author | Blanes Zamora, Sergio | es_ES |
dc.contributor.author | Ponsoda Miralles, Enrique | es_ES |
dc.date.accessioned | 2017-05-22T18:41:21Z | |
dc.date.available | 2017-05-22T18:41:21Z | |
dc.date.issued | 2014-05-15 | |
dc.identifier.issn | 0377-0427 | |
dc.identifier.uri | http://hdl.handle.net/10251/81597 | |
dc.description.abstract | [EN] We present structure preserving integrators for solving linear quadratic optimal control problems. The goal is to build methods which can also be used for the integration of nonlinear problems if they are previously linearized. The equations are solved using an iterative method on a fixed mesh with the constraint that at each iteration one can only use results obtained in previous iterations on that fixed mesh. On the other hand, this problem requires the numerical integration of matrix Riccati differential equations whose exact solution is a symmetric positive definite time-dependent matrix which controls the stability of the equation for the state. This property is not preserved, in general, by the numerical methods. We analyze how to build methods for the linear problem taking into account the previous constraints, and we propose second order exponential methods based on the Magnus series expansion which unconditionally preserve positivity for this problem and analyze higher order Magnus integrators. The performance of the algorithms is illustrated with the stabilization of a quadrotor which is an unmanned aerial vehicle. | es_ES |
dc.description.sponsorship | This work has been partially supported by Ministerio de Ciencia e Innovación (Spain) under the coordinated project MTM2010-18246-C03 and the Universitat Politècnica de València throughout the project 2087. PB also acknowledges the support through the FPU fellowship AP2009-1892. | |
dc.language | Inglés | es_ES |
dc.publisher | Elsevier | es_ES |
dc.relation.ispartof | Journal of Computational and Applied Mathematics | es_ES |
dc.rights | Reserva de todos los derechos | es_ES |
dc.subject | Nonlinear optimal control | es_ES |
dc.subject | Linear quadratic methods | es_ES |
dc.subject | Matrix Riccati differential equation | es_ES |
dc.subject | Second order exponential integrators | es_ES |
dc.subject.classification | MATEMATICA APLICADA | es_ES |
dc.title | Structure preserving integrators for solving (non-)linear quadratic optimal control problems with applications to describe the flight of a quadrotor | es_ES |
dc.type | Artículo | es_ES |
dc.type | Comunicación en congreso | |
dc.identifier.doi | 10.1016/j.cam.2013.09.061 | |
dc.relation.projectID | info:eu-repo/grantAgreement/MICINN//MTM2010-18246-C03/ | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/MECD//AP2009-1892/ES/AP2009-1892/ | es_ES |
dc.rights.accessRights | Abierto | es_ES |
dc.contributor.affiliation | Universitat Politècnica de València. Instituto Universitario de Matemática Multidisciplinar - Institut Universitari de Matemàtica Multidisciplinària | es_ES |
dc.contributor.affiliation | Universitat Politècnica de València. Escuela Técnica Superior de Ingenieros de Caminos, Canales y Puertos - Escola Tècnica Superior d'Enginyers de Camins, Canals i Ports | es_ES |
dc.contributor.affiliation | Universitat Politècnica de València. Escuela Técnica Superior de Ingeniería del Diseño - Escola Tècnica Superior d'Enginyeria del Disseny | es_ES |
dc.contributor.affiliation | Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada | es_ES |
dc.description.bibliographicCitation | Bader, P.; Blanes Zamora, S.; Ponsoda Miralles, E. (2014). Structure preserving integrators for solving (non-)linear quadratic optimal control problems with applications to describe the flight of a quadrotor. Journal of Computational and Applied Mathematics. 262:223-233. https://doi.org/10.1016/j.cam.2013.09.061 | es_ES |
dc.description.accrualMethod | S | es_ES |
dc.relation.conferencename | 13th Seminar Numerical Solution of Differential and Differential-Algebraic Equations (NUMDIFF) | |
dc.relation.conferencedate | September 10-14, 2012 | |
dc.relation.conferenceplace | Halle, Germany | |
dc.relation.publisherversion | http://dx.doi.org/10.1016/j.cam.2013.09.061 | es_ES |
dc.description.upvformatpinicio | 223 | es_ES |
dc.description.upvformatpfin | 233 | es_ES |
dc.type.version | info:eu-repo/semantics/publishedVersion | es_ES |
dc.description.volume | 262 | es_ES |
dc.relation.senia | 260474 | es_ES |
dc.identifier.eissn | 1879-1778 | |
dc.contributor.funder | Ministerio de Ciencia e Innovación | |
dc.contributor.funder | Ministerio de Educación, Cultura y Deporte |