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dc.contributor.author
Sánchez, Ignacio Julián Rodolfo
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dc.contributor.author
Louembet, Christophe
dc.contributor.author
Actis, Marcelo Jesús
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dc.contributor.author
González, Alejandro Hernán
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dc.date.available
2022-09-05T17:07:05Z
dc.date.issued
2021-03
dc.identifier.citation
Sánchez, Ignacio Julián Rodolfo; Louembet, Christophe; Actis, Marcelo Jesús; González, Alejandro Hernán; Characterization and computation of control invariant sets within target regionsfor linear impulsive control systems; Cornell University; ArXiv.org; 3-2021; 1-16
dc.identifier.issn
2331-8422
dc.identifier.uri
http://hdl.handle.net/11336/167383
dc.description.abstract
Linear impulsively controlled systems are suitable to describe a venue of real-life problems, going from disease treatment to aerospace guidance. The main characteristic of such systems is that they remain uncontrolled for certain periods of time. As a consequence, punctual equilibria characterizations outside the origin are no longer useful, and the whole concept of equilibrium and its natural extension, the controlled invariant sets, needs to be redefined. Also, an exact characterization of the admissible states, i.e., states such that their uncontrolled evolution between impulse times remain within a predefined set, is required. An approach to such tasks -- based on the Markov-Lukasz theorem -- is presented, providing a tractable and non-conservative characterization, emerging from polynomial positivity that has application to systems with rational eigenvalues. This is in turn the basis for obtaining a tractable approximation to the maximal admissible invariant sets. In this work, it is also demonstrated that, in order for the problem to have a solution, an invariant set (and moreover, an equilibrium set) must be contained within the target zone. To assess the proposal, the so-obtained impulsive invariant set is explicitly used in the formulation of a set-based model predictive controller, with application to zone tracking. In this context, specific MPC theory needs to be considered, as the target is not necessarily stable in the sense of Lyapunov. A zone MPC formulation is proposed, which is able to i) track an invariant set such that the uncontrolled propagation fulfills the zone constraint at all times and ii) converge asymptotically to the set of periodic orbits completely contained within the target zone.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Cornell University
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.subject
IMPULSIVELY CONTROLLED SYSTEMS
dc.subject
INVARIANT SETS
dc.subject
ADMISSIBLE SETS
dc.subject
MODEL PREDICTIVE CONTROL
dc.subject
POLYNOMIAL POSITIVITY
dc.subject
SEMIDEFINITE PROGRAMMING
dc.subject.classification
Matemática Aplicada
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dc.subject.classification
Matemáticas
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dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
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dc.title
Characterization and computation of control invariant sets within target regionsfor linear impulsive control systems
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2022-08-29T13:50:56Z
dc.journal.pagination
1-16
dc.journal.pais
Estados Unidos
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dc.journal.ciudad
Ithaca
dc.description.fil
Fil: Sánchez, Ignacio Julián Rodolfo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
dc.description.fil
Fil: Louembet, Christophe. Centre National de la Recherche Scientifique; Francia. Universite de Toulose - Le Mirail; Francia
dc.description.fil
Fil: Actis, Marcelo Jesús. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina
dc.description.fil
Fil: González, Alejandro Hernán. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina
dc.journal.title
ArXiv.org
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2103.13831
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/https://doi.org/10.48550/arXiv.2103.13831
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