T-singularidade: dinâmica, estabilidade e teoria de controle
| Autor(a) principal: | |
|---|---|
| Data de Publicação: | 2013 |
| Tipo de documento: | Dissertação |
| Idioma: | por |
| Título da fonte: | Repositório Institucional da UFG |
| dARK ID: | ark:/38995/00130000065hk |
| Texto Completo: | http://repositorio.bc.ufg.br/tede/handle/tede/3087 |
Resumo: | Consider a nonsmooth vector fields in R3 defined by parts on a smooth manifold of dimension one, such that it is tangent to both sides simultaneously, in fold points, visibles or invisibles. In this paper we study a local dynamics of the singularity type two-fold invisible-invisible known as Teixeira singularity, revealing new scenes of bifurcations and the nonlinear effects around the bifurcation already known, determining conditions for the existence of invariant sets (limit cycles) and the possible existence of a set with a nondeterministic chaos. Furthermore, we discuss the occurrence of this singularity in switched feedback control systems and some numerical simulations are presented. |
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Medrado, João Carlos da Rochahttp://lattes.cnpq.br/5021927574622286http://lattes.cnpq.br/1561942795469040Cespedes, Oscar Alexander Ramírez2014-09-18T15:36:44Z2013-03-22CESPEDES, Oscar Alexander Ramírez. T-singularidade: dinâmica, estabilidade e teoria de controle. 2013. 76 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2013.http://repositorio.bc.ufg.br/tede/handle/tede/3087ark:/38995/00130000065hkConsider a nonsmooth vector fields in R3 defined by parts on a smooth manifold of dimension one, such that it is tangent to both sides simultaneously, in fold points, visibles or invisibles. In this paper we study a local dynamics of the singularity type two-fold invisible-invisible known as Teixeira singularity, revealing new scenes of bifurcations and the nonlinear effects around the bifurcation already known, determining conditions for the existence of invariant sets (limit cycles) and the possible existence of a set with a nondeterministic chaos. Furthermore, we discuss the occurrence of this singularity in switched feedback control systems and some numerical simulations are presented.Quando um campo vetorial não suave é definido por partes, sobre uma variedade regular de codimensão um, esse pode ser simultaneamente tangente a ambos os lados, em pontos de dobra, visíveis ou invisíveis. Neste trabalho é estudada a dinâmica local da singularidade; tipo dobra-dobra invisível-invisível conhecida como Singularidade Teixeira, revelando novos cenários de bifurcações e os efeitos não lineares em torno da bifurcação já conhecida, determinando condições para a existência de conjuntos invariantes (ciclos limite), e a possível existência de um conjunto com uma forma não-determinística do caos. Além disso, discute-se a ocorrência de tal singularidade em sistemas de controle com retroalimentação comutante. Algumas simulações numéricas são apresentadas.Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2014-09-18T14:41:50Z No. of bitstreams: 2 Dissertacao Oscar Alexander Ramirez Cespedes.pdf: 2846357 bytes, checksum: 734d0022f388a5e80f1343acade03c64 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2014-09-18T15:36:44Z (GMT) No. of bitstreams: 2 Dissertacao Oscar Alexander Ramirez Cespedes.pdf: 2846357 bytes, checksum: 734d0022f388a5e80f1343acade03c64 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)Made available in DSpace on 2014-09-18T15:36:44Z (GMT). No. of bitstreams: 2 Dissertacao Oscar Alexander Ramirez Cespedes.pdf: 2846357 bytes, checksum: 734d0022f388a5e80f1343acade03c64 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2013-03-22Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPqapplication/pdfhttp://repositorio.bc.ufg.br/tede/retrieve/7920/Dissertacao%20Oscar%20Alexander%20Ramirez%20Cespedes.pdf.jpgporUniversidade Federal de GoiásPrograma de Pós-graduação em Matemática (IME)UFGBrasilInstituto de Matemática e Estatística - IME (RG)[1] A.S. HODEL, C. H. Variable-structure pid control to prevent integrator windup. IEEE Trans. Ind. Electron, 48:442–451, 2001. [2] BROGLIATO, B. Nonsmooth Mechanics — Models Dynamics and Control. Springer-Verlag, London, second edition, 1999. [3] BROGLIATO, B. Impacts in Mechanical Systems — Analysis and Modelling in:: Lecture Notes in Physics. Springer-Verlag, New York, first edition, 2000. [4] E A. COLOMBO, M. J. The two fold singularity of discontinuous vector fields. SIAM J. Appl. Dyn. Syst., (5):624–640, 2009. [5] E. CONTE, A. F; ZBILUT, J. P. On a simple case of possible non-deterministic chaotic behavior in compartment theory of biological observables,. Chaos Solitons Fractals, (22):277–284, 2004. [6] FEO, O. D. Modeling diversity by strange attractors with application to temporal pattern recognition. (Tesis Doctoral):École Politechnique Fédérale de Lausanne, 2001. [7] FILIPPOV, A. F. Differential Equations with Discontinuous Righthand Sides. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1988. [8] GATTO, M; MANDRIOLI, D. Pseudoequilibrium in dynamical systems. Int. J. Systems Sci., (4):809–824, 1973. [9] GUCKENHEIMER, J; HOLMES, P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Applied Mathematical Sciences; 42). Springer-Verlag, New York, first edition, 1983. [10] JEFFREY, M. R. Non determinism in the limit of nonsmooth dynamics. SIAM J. Applied Dynamical Systems, 10(2):423–451, 2011. [11] JEFFREY, M; FERNÁNDEZ-GARCÍA, S. Structural stability of the two-fold singularity. SIAM J. Appl. Dyn. Syst., (5):624–640, 2012. [12] J.P. HESPANHA, A. M. Switching between stabilizing controllers. Automatica, volume = 38, number = 11, pages = 1905-1917, 2002. [13] KUZNETSOV, Y. A. Elements of Applied Bifurcation Theory. Springer-Verlag, New York, third edition, 2004. [14] MEISS, J. D. Differential Dynamical Systems. AM Monogr. Math. Comput. 14, SIAM, Philadelhia, 2007. [15] P. T. PIIROINEN, Y. A. K. An event-driven method to simulate filippov systems with accurate computing of sliding motions. ACM Trans. Math. Software, (34):article 13, 2008. [16] SOTOMAYOR, J. Lições de Equações Diferenciais Ordinárias. Projeto Euclides, Rio de Janeiro, first edition, 1979. [17] TEIXEIRA, M. A. Generic bifurcation of sliding vector fields. J. Math. Anal. Appl., (176):436–457, 1993. [18] TEIXEIRA, M. Stability conditions for discontinuous vector fields. J. Differ. Equations, (88):15–29, 1990. [19] UTKIN, V. Variable structure systems with sliding modes. Automatic Control, IEEE Transactions on, 22(2):212–222, 1977. [20] UTKIN, V. Vss premise in xx century: Evidences of a witness. proceedings of the 6th ieee international workshop on variable structure systems. 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T-singularidade: dinâmica, estabilidade e teoria de controle |
| dc.title.alternative.eng.fl_str_mv |
T-singularity: dynamics, stability and control theory |
| title |
T-singularidade: dinâmica, estabilidade e teoria de controle |
| spellingShingle |
T-singularidade: dinâmica, estabilidade e teoria de controle Cespedes, Oscar Alexander Ramírez T-singularidade Dinâmica Estabilidade e teoria de controle T-singularity Dynamics Stability and control theory CIENCIAS EXATAS E DA TERRA::MATEMATICA |
| title_short |
T-singularidade: dinâmica, estabilidade e teoria de controle |
| title_full |
T-singularidade: dinâmica, estabilidade e teoria de controle |
| title_fullStr |
T-singularidade: dinâmica, estabilidade e teoria de controle |
| title_full_unstemmed |
T-singularidade: dinâmica, estabilidade e teoria de controle |
| title_sort |
T-singularidade: dinâmica, estabilidade e teoria de controle |
| author |
Cespedes, Oscar Alexander Ramírez |
| author_facet |
Cespedes, Oscar Alexander Ramírez |
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author |
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Medrado, João Carlos da Rocha |
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http://lattes.cnpq.br/5021927574622286 |
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http://lattes.cnpq.br/1561942795469040 |
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Cespedes, Oscar Alexander Ramírez |
| contributor_str_mv |
Medrado, João Carlos da Rocha |
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T-singularidade Dinâmica Estabilidade e teoria de controle |
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T-singularidade Dinâmica Estabilidade e teoria de controle T-singularity Dynamics Stability and control theory CIENCIAS EXATAS E DA TERRA::MATEMATICA |
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T-singularity Dynamics Stability and control theory |
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CIENCIAS EXATAS E DA TERRA::MATEMATICA |
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Consider a nonsmooth vector fields in R3 defined by parts on a smooth manifold of dimension one, such that it is tangent to both sides simultaneously, in fold points, visibles or invisibles. In this paper we study a local dynamics of the singularity type two-fold invisible-invisible known as Teixeira singularity, revealing new scenes of bifurcations and the nonlinear effects around the bifurcation already known, determining conditions for the existence of invariant sets (limit cycles) and the possible existence of a set with a nondeterministic chaos. Furthermore, we discuss the occurrence of this singularity in switched feedback control systems and some numerical simulations are presented. |
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2013 |
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2013-03-22 |
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CESPEDES, Oscar Alexander Ramírez. T-singularidade: dinâmica, estabilidade e teoria de controle. 2013. 76 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2013. |
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ark:/38995/00130000065hk |
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CESPEDES, Oscar Alexander Ramírez. T-singularidade: dinâmica, estabilidade e teoria de controle. 2013. 76 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2013. ark:/38995/00130000065hk |
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por |
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[1] A.S. HODEL, C. H. Variable-structure pid control to prevent integrator windup. IEEE Trans. Ind. Electron, 48:442–451, 2001. [2] BROGLIATO, B. Nonsmooth Mechanics — Models Dynamics and Control. Springer-Verlag, London, second edition, 1999. [3] BROGLIATO, B. Impacts in Mechanical Systems — Analysis and Modelling in:: Lecture Notes in Physics. Springer-Verlag, New York, first edition, 2000. [4] E A. COLOMBO, M. J. The two fold singularity of discontinuous vector fields. SIAM J. Appl. Dyn. Syst., (5):624–640, 2009. [5] E. CONTE, A. F; ZBILUT, J. P. On a simple case of possible non-deterministic chaotic behavior in compartment theory of biological observables,. Chaos Solitons Fractals, (22):277–284, 2004. [6] FEO, O. D. Modeling diversity by strange attractors with application to temporal pattern recognition. (Tesis Doctoral):École Politechnique Fédérale de Lausanne, 2001. [7] FILIPPOV, A. F. Differential Equations with Discontinuous Righthand Sides. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1988. [8] GATTO, M; MANDRIOLI, D. Pseudoequilibrium in dynamical systems. Int. J. Systems Sci., (4):809–824, 1973. [9] GUCKENHEIMER, J; HOLMES, P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Applied Mathematical Sciences; 42). Springer-Verlag, New York, first edition, 1983. [10] JEFFREY, M. R. Non determinism in the limit of nonsmooth dynamics. SIAM J. Applied Dynamical Systems, 10(2):423–451, 2011. [11] JEFFREY, M; FERNÁNDEZ-GARCÍA, S. Structural stability of the two-fold singularity. SIAM J. Appl. Dyn. Syst., (5):624–640, 2012. [12] J.P. HESPANHA, A. M. Switching between stabilizing controllers. Automatica, volume = 38, number = 11, pages = 1905-1917, 2002. [13] KUZNETSOV, Y. A. Elements of Applied Bifurcation Theory. Springer-Verlag, New York, third edition, 2004. [14] MEISS, J. D. Differential Dynamical Systems. AM Monogr. Math. Comput. 14, SIAM, Philadelhia, 2007. [15] P. T. PIIROINEN, Y. A. K. An event-driven method to simulate filippov systems with accurate computing of sliding motions. ACM Trans. Math. Software, (34):article 13, 2008. [16] SOTOMAYOR, J. Lições de Equações Diferenciais Ordinárias. Projeto Euclides, Rio de Janeiro, first edition, 1979. [17] TEIXEIRA, M. A. Generic bifurcation of sliding vector fields. J. Math. Anal. Appl., (176):436–457, 1993. [18] TEIXEIRA, M. Stability conditions for discontinuous vector fields. J. Differ. Equations, (88):15–29, 1990. [19] UTKIN, V. Variable structure systems with sliding modes. Automatic Control, IEEE Transactions on, 22(2):212–222, 1977. [20] UTKIN, V. Vss premise in xx century: Evidences of a witness. proceedings of the 6th ieee international workshop on variable structure systems. World Scientific, p. 1–34, 2000. |
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Repositório Institucional da UFG |
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http://repositorio.bc.ufg.br/tede/bitstreams/67866888-97a7-4792-bd06-8b52e1064c35/download http://repositorio.bc.ufg.br/tede/bitstreams/de0d3970-d9f6-407b-8379-fc881988b8e5/download http://repositorio.bc.ufg.br/tede/bitstreams/bb517f30-f520-47e9-9237-62885c1bcdb4/download http://repositorio.bc.ufg.br/tede/bitstreams/1d84d0d7-cbae-433c-b11e-4980d7555b0c/download http://repositorio.bc.ufg.br/tede/bitstreams/f76ede9f-fc66-487b-96a3-d2fab3edf58d/download http://repositorio.bc.ufg.br/tede/bitstreams/f070b0c6-46ab-4f3b-9381-92f9b14aa925/download http://repositorio.bc.ufg.br/tede/bitstreams/b10d25d0-806c-4cc8-a041-addb9e78f108/download |
| bitstream.checksum.fl_str_mv |
bd3efa91386c1718a7f26a329fdcb468 4afdbb8c545fd630ea7db775da747b2f 1e0094e9d8adcf16b18effef4ce7ed83 9da0b6dfac957114c6a7714714b86306 734d0022f388a5e80f1343acade03c64 2936251c9a4f7801667fe3f58b5b667b 9b272616eaf5d7a318af97ac6cf86ec4 |
| bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 MD5 MD5 MD5 MD5 |
| repository.name.fl_str_mv |
Repositório Institucional da UFG - Universidade Federal de Goiás (UFG) |
| repository.mail.fl_str_mv |
tasesdissertacoes.bc@ufg.br |
| _version_ |
1815172575562563584 |