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: 2013-03-22 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / 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. / 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.
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.bc.ufg.br:tede/3087 |
| Date | 22 March 2013 |
| Creators | Cespedes, Oscar Alexander Ramírez |
| Contributors | Medrado, João Carlos da Rocha |
| Publisher | Universidade Federal de Goiás, Programa de Pós-graduação em Matemática (IME), UFG, Brasil, Instituto de Matemática e Estatística - IME (RG) |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | Portuguese |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/masterThesis |
| Format | application/pdf |
| Source | reponame:Biblioteca Digital de Teses e Dissertações da UFG, instname:Universidade Federal de Goiás, instacron:UFG |
| Rights | http://creativecommons.org/licenses/by-nc-nd/4.0/, info:eu-repo/semantics/openAccess |
| Relation | 6600717948137941247, 600, 600, 600, 600, -4268777512335152015, -7090823417984401694, -2555911436985713659, [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. |
Page generated in 0.0026 seconds