Victor Alberto Jose Ayala Bravo

Pós-doutorado

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Áreas de atuação

Organização de eventos

Participação em eventos

Orientou

Produções bibliográficas

• AYALA, VICTOR ; RIBEIRO, RODOLFO ; SAN MARTIN, LUIZ A. B. . Controllability on $mathrm{Sl}(2,mathbb{C})$ with Restricted Controls. SIAM Journal on Control and Optimization , v. 52, p. 2548-2567, 2014.

• AYALA, V. ; KAWAN, C. . Topological conjugacy of real projective flows. Journal of the London Mathematical Society , v. 90, p. 49-66, 2014.

• AYALA, V. ; JIRON, I. . Linear flows and Morse graphs:Topological consequences in low dimensions. Linear Algebra and its Applications , v. 1, p. 2177-2194, 2013.

• AYALA, V. ; Kizil, E ; Null controllability on Lie groups. Proyecciones (Antofagasta. Impresa) , v. 32, p. 61-72, 2013.

• AYALA, V. ; RODRIGUEZ, J. . Optimal trajectories for angular systems on the projective line. Optimal Control Applications and Methods , v. 33, p. 199-213, 2012.

• AYALA, V. ; RODRÍGUEZ, J. C. ; TRIBUZY, I. A. ; WAGNER, C. . Solutions of singular control systems on lie groups. Journal of Dynamical and Control Systems , v. 18, p. 323-338, 2012.

• AYALA, VÍCTOR ; KIZIL, EYÜP ; DE AZEVEDO TRIBUZY, IVAN . On an algorithm for finding derivations of Lie algebras. Proyecciones (Antofagasta. Impresa) , v. 31, p. 81-90, 2012.

• AYALA, V. ; KLIEMANN, W. ; VERA, F. . Isochronous sets of invariant control systems on Lie groups. Systems & Control Letters (Print) , v. 60, p. 937-942, 2011.

• AYALA, V. ; RODRIGUEZ, J. ; San Martín, L. . Optimality on homogeneous space. An example on the real projective line. SIAM Journal on Control and Optimization (Print) , v. 29, p. 1515-1528, 2010.

• AYALA, V ; RODRÍGUEZ, J. C ; SAN MARTÍN, L. A. B . EXTREMALS OF A QUADRATIC COST OPTIMAL PROBLEM ON THE REAL PROJECTIVE LINE. Proyecciones (Antofagasta. Impresa) , v. 29, p. 145-164, 2010.

• AYALA, V. ; José Ayala-Hoffmann ; Ivan Tribuzy . Controllability of Invariant Control Systems at Uniform Time. Kybernetika (Praha) , v. 1, p. 405, 2009.

• AYALA, V. ; Ivan Tribuzy . On a charaterization of Riemann manifolds. Proyecciones (Antofagasta. Impresa) , v. 27, p. 113-144, 2008.

• AYALA, V. ; Marcos M. Diniz ; Ivan Tribuzy ; José M. M. Veloso . Wave front sets singularities of. Cubo (Temuco) , v. 1, p. 235-257, 2008.

• AYALA, V. ; COLONIUS, F. ; KLIEMANN, W. . On Topological Equivalence of Linear Flows with Applications to Bilinear Control Systems. Journal of Dynamical and Control Systems , v. 13, p. 313-336, 2007.

• AYALA, V. ; COLONIUS, F. ; KLIEMANN, W. . Dynamical characterization of the Lyapunov form of matrices. Linear Algebra and its Applications , v. 402, p. 272-290, 2005.

• AYALA, V. ; KLIEMANN, W. ; San Martín, L. . Control sets and total positivity. Semigroup Forum , v. 69, p. 113-140, 2004.

• AYALA, V. ; SOLIS, G. ; Femat, R. ; KLIEMANN, W. . Complete Synchronizability of Chaotic Systems: A Geometric Approach. Chaos, Solitons and Fractals , v. 13, p. 495-501, 2003.

• AYALA, V. ; KLIEMANN, W. . A Descomposition Theorem for Singular Control Systems on Lie Groups. Computers & Mathematics with Applications (1987) , v. 45, p. 635-646, 2003.

• AYALA, V. ; San Martín, L. . Controllability Properties of a Class of Control Systems on Lie Groups.. Lecture Notes in Control and Information Sciences , v. 1, p. 83-92, 2001.

• AYALA, V. ; KIZIL, E. . Observability of General Linear Pairs. Computers & Mathematics with Applications , v. 39, p. 35-43, 2000.

• AYALA, V. ; KIZIL, E. ; ZEGARRA, R. . Transitivity of Linear Control Systems on Lie Groups. Journal of Computational and Applied Mathematics , v. 18, p. 1-9, 1999.

• AYALA, V. ; San Martín, L. . Controllability of two-dimensional Bilinear Systems: Restricted Controls, Discrete Time. Proyecciones (Antofagasta. Impresa) , v. 18, p. 207-223, 1999.

• AYALA, V. . Linear Control Systems on Lie Groups and Controllability. Proceedings of Symposia in Pure Mathematics , v. 64, p. 47-64, 1999.

• AYALA, V. ; ROJO, O. ; SOTO, R. . Observability of The Direct product of Bilinear Control Systems on Lie Groups. Computers & Mathematics with Applications , v. 36, p. 107-112, 1998.

• AYALA, V. ; HACIBEKIROGLU, A. . Local Observability of Invariant Dynamics on Compact Lie Groups with Square Integrable Output Map Functions. Computers & Mathematics with Applications , v. 34, p. 61-70, 1997.

• AYALA, V. ; HACIBEKIROGLU, A. . Examples of Linear Control Systems on Lie Groups. Pro Mathematica (Lima) , v. 10, p. 230-249, 1996.

• AYALA, V. . Controllability of Nilpotent Systems. Banach Center Publications , v. 32, p. 35-46, 1995.

• AYALA, V. ; HACIBEKIROGLU, A. . Observability of Linear Control Systems on Lie Groups. International Atomic Energy Agency. Technical Document , v. 1, p. 1-18, 1995.

• AYALA, V. ; TIRAO, J. . Controllability of Linear Vector Fields on Line Groups. International Atomic Energy Agency. Technical Document , v. 1, p. 1-24, 1994.

• AYALA, V. . Involutive Co-Distribution Preserved by Transitive Families. Proyecciones (Antofagasta) , v. 13, p. 35-52, 1994.

• AYALA, V. ; JIRON, I. . Observabilidad del Producto directo de Sistemas Bilineales. Cubo (Temuco) , v. 9, p. 35-46, 1993.

• AYALA, V. ; VERGARA, L. . Invariant Control Systems on Nilpotent Lie Groups. International Atomic Energy Agency. Technical Document , v. 1, p. 1-15, 1993.

• AYALA, V. . Controllability and The Rank Conditions of the Control Vectors. Computers & Mathematics with Applications (1987) , v. 11, p. 41-44, 1992.

• AYALA, V. ; VERGARA, L. . Co-Adjoint Representation and Controllability. Proyecciones (Antofagasta) , v. 11, p. 37-48, 1992.

• AYALA, V. ; San Martín, L. . Minimal realization under controllability. Systems & Control Letters (Print) , v. 16, p. 289-293, 1991.

• AYALA, V. . Integrabilidade de Distribuçoes, Classes de Inobservabilidade. Proceedings of the American Mathematical Society , v. 1, p. 67-78, 1988.

• AYALA, V. ; San Martín, L. . Grupos de Lie (Ph D Course Monography). Departamento de Matemática, UCN, 2002.

• AYALA, V. . Diferenciabilidad en Espacios Euclideanos (Licenciatura Course Monography). Departamento de Matemática, UCN, 1998.

• AYALA, V. ; COLONIUS, F. ; KLIEMANN, W. . Dynamos of Bilinear Control Systems. In preparation for Lecture Notes in Mathematics, 1998.

• AYALA, V. ; COLONIUS, F. ; KLIEMANN, W. . Towards a Topological Equivalence of Bilinear Control Systems. In: 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2006), 2006, Kyoto. Proceeding of MTNS 2006, 2006. v. 1. p. 234-241.

• AYALA, V. ; KLIEMANN, W. . Lyapunov Decomposition and Spectra on Flag Manifolds. In: XIII Congresso de Matemática, Capricórnio, 2003, Antofagasta. XIII Congresso de Matemática, Capricórnio, 2003. p. 1.

• AYALA, V. . Contribuciones a la Teoría Geométrica de Sistemas de Control. In: XIII Congresso de Matemática, Capricórnio, 2003, Antofagasta. XIII Congresso de Matemática, Capricórnio, 2003. p. 1.

• AYALA, V. ; KLIEMANN, W. . Lyapunov Normal Form of Matrices. In: Workshop in Control Theory, 2002, Campinas. Workshop in Control Theory, 2000. p. 1.

• AYALA, V. . Matrices Totalmente Positivas, una Visión desde la Geometría Diferemncial. In: XV Jornada de Matematica de la Zona Sur, 2001. Lemma type of Poletskii for the quasiregular mapping on the Heisenberg. p. 25'-27.

• AYALA, V. . Descomposición de Sistemas Singulares. In: X Congresso de Matemática, Capricórnio, 2001, Antofagasta. X Congresso de Matemática, Capricórnio, 2001. p. 1.

• AYALA, V. . Ciertas Clases de Sistemas de Control Sobre Grupos de Lie.. In: X Congresso de Matemática, Capricórnio, 2001, Antofagasta. X Congresso de Matemática, Capricórnio, 2001. p. 1.

• AYALA, V. . Controllability Properties of Class of Control Systems. In: Catalogue de documents pour le chercheur, 2000, Paris. Lecture notes in control and information sciences, 2000. v. 1. p. 83-92.

• AYALA, V. ; Ivan Tribuzy ; José M. M. Veloso . Optimal control and sub-Riemannian distributions for a class of control systems. Cubo (Temuco) , 2009.

• AYALA, V. ; José Ayala-Hoffmann ; Ivan Tribuzy . Controllability of Invariant control systems at uniform time. Kybernetika (Praha) , 2009.

• Ivan Tribuzy ; AYALA, V. . On charaterization of Riemann manifolds. Proyecciones (Antofagasta) , 2008.

• AYALA, V. ; KIZIL, E. . 0-controllability of linear control systems on nilpotent Lie groups. Proyecciones (Antofagasta) , 2008.

• AYALA, V. ; Marcos M. Diniz ; José M. M. Veloso ; José C. P. Lima ; Ivan Tribuzy . Wave front sets singularities of homogeneous sub-Riemannian three dimensional manifolds. Cubo (Temuco) , 2008.

• AYALA, V. . The Locus of an Almost Riemannian Structure. 2015. (Apresentação de Trabalho/Conferência ou palestra).

• AYALA, V . Contribuciones a la Teoría Geométrica de los Sistemas de Control. 2014. (Apresentação de Trabalho/Congresso).

• AYALA, V . Sistemas de Controle e Aplicacoes. 2014. (Apresentação de Trabalho/Conferência ou palestra).

• AYALA, V . Almost Riemannian Structures and Linear Control Systems on Lie Groups. 2014. (Apresentação de Trabalho/Congresso).

• AYALA, V . Linear Control Systems on Lie Groups and Applications. 2014. (Apresentação de Trabalho/Conferência ou palestra).

• AYALA, V . Almost Riemannian Structures. 2014. (Apresentação de Trabalho/Congresso).

• AYALA, V. . Teoría de Morse y sistemas de control bilineales. 2007. (Apresentação de Trabalho/Congresso).

• AYALA, V. . Equivalencia topológica y grafos. 2007. (Apresentação de Trabalho/Congresso).

• AYALA, V. . Towards to Topolocgical Classification of Bilinear Control Systems. 2006. (Apresentação de Trabalho/Congresso).

• AYALA, V. . Equivalencia de Sistemas Bilineares. 2006. (Apresentação de Trabalho/Congresso).

• AYALA, V. . Equivalencia topológica de semigrupos. 2005. (Apresentação de Trabalho/Congresso).

• AYALA, V. . Geometría y Sistemas de Control. 2005. (Apresentação de Trabalho/Outra).

• AYALA, V. . Contribuciones a la teoría geométrica de sistemas de control. 2003. (Apresentação de Trabalho/Congresso).

• AYALA, V. . Sistemas Singulares 2.Sistemas Lineares. 2001. (Apresentação de Trabalho/Congresso).

• AYALA, V. . Matrices totalmente positivas, una visión desde la Geometría Diferencial. 2001. (Apresentação de Trabalho/Congresso).

• AYALA, V. . Geometria Diferencial y Control. 2001. (Apresentação de Trabalho/Seminário).

• AYALA, V. . Controllability Properties of a Class of Control Systems. 2000. (Apresentação de Trabalho/Outra).

• AYALA, V. . Conferencia: Ciertas Clases de Sistema de Control Sobre Grupos de Lie.. 2000. (Apresentação de Trabalho/Congresso).

Projetos de pesquisa

• 2015 - Atual

  Linear Control Systems on Lie Groups. Sub-Riemannian Geometry. Optimality and Semigroups, Descrição: The main aim of the proposal is to give a contribution to the Differential Geometry Control System Theory, through the class of Linear Control Systems on Lie Groups (LCS). This class of system was introduced by our team in [5]. The project contains a number of open problems from both, new and old challenges. The proposal is based on a series of papers, coming from our previous Fondecyt projects, see [5] up to [27], and the unpublished research mentioned in the Work in Progress section of the project. Next, we list the specific goals of the proposal through six different but some of theme related problems. I. Almost Riemannian and SubRiemannian Structures (ARS, SRE). It turns out that a LCS is a bonafide family of ARS. First, we would like to understand this structure. To work out the associated "metric" and the normal topics related, for instance the geodesics. In particular, on Lie groups of low dimension. Second, any ARS can be lifted to a sub-Riemannian structure, a geometry closely related to optimal control theory, see [1] up to [4]. In fact, we already now that an ARS can be lifted to Sub- Riemannian structure. We propose to explore this situation deeply, by the lifting and the projection. Furthermore, we also propose to begin a very hard challenge: to explore the existence of a meaning for a Gauss-Bonnett or/and a Gauss-Bonnet-Chern theorem for a LCS, if something like that really exists, see the article A Gauss Bonnet-like formula on two-dimensional almost-Riemannian manifolds, [4]. II. Optimal Control for LCS. The time-optimal and quadratic ones, are always at the heart of control problems, they light up the essential controllability question. We expect to establish the Pontryagin Maximum Principle for LCS. We also need a version of this principal to compute the geodesics of an ARS. III. Equivalence Theorem Extensions. In [47] Jouan proved a fundamental result in our theory: a control affine system on a differentiable manifold M is equivalent by a diffeomorphism ψ to a linear system on a Lie group or a homogeneous space if and only if the vector fields of the system are complete and generate a finite dimensional Lie algebra. We expect to extend this results in several directions. From the group G to a homogeneous space G/H. From a LCS to a Singular Control System. And, for an arbitrary ARS, i.e., by considering a family {f₁,?,fn}} of vector fields on a manifold M as an orthonormal frame, when they generate a finite dimensional lie algebra. IV. Controllability and Stability of LCS and Singular Control Systems (SCS). It turns out that to characterize a global geometric property of a LCS is a real challenge. We propose to study both properties according to the different classes of Lie groups. V. Bilinear Control Systems (BCS). BCS provide a large class of systems with a wide range of applications, including nonlinear systems linearized at fixed point with respect to the variable state. Controllability of BCS has received a substantial amount of interest over the last 30 years, but general characterizations of complete controllability for this class of systems are still not available. Most of the approaches to this problem are algebraic in nature, [40]. We propose to approach this topic from Conley- Morse and Colonius-Kliemann theory, [35]. VI. Lie Semigroups and Control Systems. Any semisimple connected Lie group G is associated to a relevant class of compact cosets: Grassmannians and flag manifolds, [65]. We propose, to approach control theory from the dynamical system point of view (Lyapunov spectrum, Morse decomposition, chain recurrent components and the asymptotic behavior of the system). To analyze semigroups from their control sets. To obtain controllability results for invariant systems in low dimension of Lie groups and their homogeneous spaces. Methodology-Activities The Proposal consider a 20 hrs a week of work by the main researcher. The supervision of 2 doc. , Situação: Em andamento; Natureza: Pesquisa. , Integrantes: Victor Alberto Jose Ayala Bravo - Coordenador / J. Rodriguez - Integrante / Luiz San Martin - Integrante / Philippe Jouan - Integrante / Adriano Da Silva - Integrante.

• 2010 - 2014

  Fondecyt/1100375, Descrição: Geometric control Systems: Topological Equivalence, controllability, Stability and Optmality.. , Situação: Concluído; Natureza: Pesquisa. , Integrantes: Victor Alberto Jose Ayala Bravo - Coordenador.

• 2006 - 2009

  Fondecyt/1060977 - Cohomologically Rigid Z-Actions On Compact Solvmanifolds. Control Systems On LIe Groups: Foliations and Convering Spaces., Situação: Concluído; Natureza: Pesquisa. , Integrantes: Victor Alberto Jose Ayala Bravo - Coordenador., Financiador(es): Universidad Catolica Del Norte - Auxílio financeiro.

• 2006 - 2008

  Fondecyt / 1060981 - Control Sets and Spectrum Approach to semigroup and dynamical systems. Pontryagin maximum principle on homogeneous spaces., Situação: Concluído; Natureza: Pesquisa. , Integrantes: Victor Alberto Jose Ayala Bravo - Coordenador., Financiador(es): Universidad Catolica Del Norte - Cooperação / FONDECYT - Bolsa.

• 2005 - 2007

  FORTALECIMIENTO DEL PROGRAMA DE DOCTORADO EN CIENCIAS MENCION MATEMATICA DE LA UNIVERSIDAD CATOLICA DEL NORTE, Situação: Em andamento; Natureza: Pesquisa. , Integrantes: Victor Alberto Jose Ayala Bravo - Coordenador., Financiador(es): Fundacion Andes - Auxílio financeiro.

• 2002 - 2006

  Fondecyt/1020439 - Optimal Problems of Linear control sytems on lie Groups totally positive matrices and control sets., Situação: Concluído; Natureza: Pesquisa. , Integrantes: Victor Alberto Jose Ayala Bravo - Coordenador., Financiador(es): Universidad Catolica Del Norte - Cooperação.

• 2002 - 2006

  Fondecyt/7020439 - Incentivo a la cooperación international. Proyecto complementario., Situação: Concluído; Natureza: Pesquisa. , Integrantes: Victor Alberto Jose Ayala Bravo - Coordenador., Financiador(es): Universidad Catolica Del Norte - Cooperação.

• 1999 - 2001

  Fondecyt/1990360 - Singular Control Systems on Lie Groups., Situação: Concluído; Natureza: Pesquisa. , Integrantes: Victor Alberto Jose Ayala Bravo - Coordenador., Financiador(es): Universidad Catolica Del Norte - Cooperação.

• 1999 - 2001

  Fondecyt/7990009 - Incentivo A La Cooperación International Proyecto Complementario., Situação: Concluído; Natureza: Pesquisa. , Integrantes: Victor Alberto Jose Ayala Bravo - Coordenador., Financiador(es): Universidad Catolica Del Norte - Cooperação.

• 1999 - 2001

  Fondecyt/1990361 - MAtrix Inverse Eigenvalue Problems Applied to Discrete Inverse Problems In Vibration., Situação: Concluído; Natureza: Pesquisa. , Integrantes: Victor Alberto Jose Ayala Bravo - Coordenador., Financiador(es): Universidad Catolica Del Norte - Cooperação.

• 1996 - 1998

  Fondecyt/1960641 - Aproximación Nilpotente Y Controlabilidad de Sistemas Lineales En Grupos de Lie,, Situação: Concluído; Natureza: Pesquisa. , Integrantes: Victor Alberto Jose Ayala Bravo - Coordenador., Financiador(es): Universidad Catolica Del Norte - Cooperação.

Prêmios