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Structure preserving integrators for solving (non-)linear quadratic optimal control problems with applications to describe the flight of a quadrotor

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Structure preserving integrators for solving (non-)linear quadratic optimal control problems with applications to describe the flight of a quadrotor

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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


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