Controlabilidad de ecuaciones diferenciales retardadas semilineales impulsivas con retardo infinito y condiciones no locales

Autores/as

DOI:

https://doi.org/10.37135/ns.01.10.01

Palabras clave:

condiciones no locales, controlabilidad, ecuaciones retardadas semilineales, impulsos, retardo infinito, teorema del punto fijo de Rothe

Resumen

En este artículo, se prueba la controlabilidad exacta de ecuaciones retardadas semilineales con retardo infinito, impulsos y condiciones no locales; probando la conjetura que afirma que la controlabilidad se preserva bajo la influencia de retardo, impulsos y condiciones no locales si se asumen algunas condiciones sobre los términos no lineales. Como una aplicación de este resultado, se presenta un ejemplo donde todas las condiciones asumidas se satisfacen.

Descargas

Los datos de descargas todavía no están disponibles.

Citas

Banas, J., & Goebel, K. (1980). Measures of Noncompactness in Banach Spaces. In Lecture Notes in Pure and Applied Mathematics (Vol. 60). New York USA: Marcel Dekker, Inc.

Carrasco, A., Leiva, H., Sanchez, J. L., & Tineo, A. (2014). Approximate Controllability of the Semilinear Impulsive Beam Equation with Impulses. Transaction on IoT and Cloud Computing, 2(3), 70–88.

Chukwu, E. N. (1979). Controllability of Delay Systems with Restrained Controls. Journal of Optimization Theory and Applications, 29(2), 301–320. Recuperado de https://link.springer.com/article/10.1007/BF00937172

Chukwu, E. N. (1980). On the Null-Controllability of Nonlinear Delay Systems with Restrained Controls. Journal of Mathematical Analysis and Applications, 76, 283–296. Recuperado de https://www.sciencedirect.com/science/article/pii/0022247X80900785/pdf?md5=c130e553ddc226dcf729e79f71d89a5a&pid=1-s2.0-0022247X80900785-main.pdf

Chukwu, E. N. (1987). Global Null Controllability of Nonlinear Delay Equations with Controls in a Compact Set. Journal of Optimization Theory and Applications, 53(1), 43–57. Recuperado de https://link.springer.com/article/10.1007/BF00938816

Chukwu, E. N. (1991). Nonlinear Delay Systems Controllability. Journal of Mathematical Analysis and Applications, 162(2), 564–576. https://doi.org/https://doi.org/10.1016/0022-247X(91)90169-Z

Chukwu, E. N. (1992). Stability and Time-Optimal Control of Hereditary Systems. In E. N. Chukwu (Ed.), Mathematics in Science and Engineering (Vol. 188). Elsevier. https://doi.org/https://doi.org/10.1016/S0076-5392(09)60165-X

Coron, J. M. (2007). Control and Nonlinearity. In Mathematical Surveys and Monographs (Vol. 136). Provience, RI: American Mathematical Society. Recuperado de https://bookstore.ams.org/surv-136-s/

Curtain, R. F., & Pritchard, A. J. (1978). Infinite Dimensional Linear Systems. In Lecture Notes in Control and Information Sciences (Vol. 8). Berlin Heidelberg: Springer Verlag. https://doi.org/https://doi.org/10.1007/BFb0006761

Curtain, R. F., & Zwart, H. J. (1995). An Introduction to Infinite Dimensional Linear Systems Theory. In Text in Applied Mathematics (Vol. 21). New York USA: Springer Verlag. https://doi.org/https://doi.org/10.1007/978-1-4612-4224-6

Dauer, J. P. (1976). Nonlinear Perturbation of Quasilinear Control Systems. Journal of Mathematical Analysis and Applications, 54(3), 717–725. Recuperado de https://www.sciencedirect.com/science/article/pii/0022247X76901918/pdf?md5=91086738c9fa51fc1d5571505866f4d2&pid=1-s2.0-0022247X76901918-main.pdf

Do, V. N. (1990). Controllability of Semilinear Systems. Journal of Optimization Theory and Applications, 65(1), 41–52. https://doi.org/https://doi.org/10.1007/BF00941158

Hale, J., & Kato, J. (1978). Phase space for retarded equations with infinite delay. Funkcialaj Ekvacioj, 21(1), 11–41. Recuperado de http://fe.math.kobe-u.ac.jp/FE/FE_pdf_with_bookmark/FE21-30-en_KML/fe21-011-041/fe21-011-041.pdf

Isac, G. (2004). On Rothe’s fixed point theorem in General Topological Vector Space. Analele Stiintifice Ale Universitatii Ovidius Constanta, 12(2), 127–134. Recuperado de https://www.anstuocmath.ro/mathematics/pdf8/127_134_GIsac.pdf

Lee, E. B., & Markus, L. (1967). Foundations of Optimal Control Theory. New York USA: Wiley. Recuperado de https://www.semanticscholar.org/paper/Foundations-of-optimal-control-theory-Lee-Markus/5a51f2611dca07aa2705565a297b483c9b6b25de

Leiva, H. (2014a). Controllability of Semilinear Impulsive Nonautonomous Systems. International Journal of Control, 88(3). https://doi.org/https://doi.org/10.1080/00207179.2014.

Leiva, H. (2014b). Rothe’s fixed point theorem and Controllability of Semilinear Nonautonomous Systems. System & Control Letters, 67, 14–18. https://doi.org/https://doi.org/10.1016/j.sysconle.2014.01.008

Leiva, H. (2015). Approximate Controllability of Semilinear Impulsive Evolution Equations. Abstract and Applied Analysis, 2015. https://doi.org/https://doi.org/10.1155/2015/797439

Leiva, H. (2018). Karakostas Fixed Point Theorem and the Existence of Solutions for Impulsive Semilinear Evolution Equations with Delays and Nonlocal Conditions. Communications in Mathematical Analysis, 21(2), 68–91. Recuperado de https://projecteuclid.org/journals/communications-in-mathematical-analysis/volume-21/issue-2/Karakostas-Fixed-Point-Theorem-and-the-Existence-of-Solutions-for/cma/1547262053.short

Leiva, H., & Merentes, N. (2015). Approximate Controllability of the Impulsive Semilinear Heat Equation. Journal of Mathematics and Applications, 38, 85–104. Recuperado de https://jma.prz.edu.pl/fcp/FGBUKOQtTKlQhbx08SlkTUQJQX2o8DAoHNiwFE1xVS3tBG1gnBVcoFW8SETZKHg/26/sdudek%40prz.edu.pl/jma-38/jma38_08_leiva.pdf

Leiva, H., & Zambrano, H. (1999). Rank condition for the controllability of a linear time-varying system. International Journal of Control, 72(10), 929–931. https://doi.org/https://doi.org/10.1080/002071799220669

Liu, J. H. (2000). Periodic solutions of infinite delay evolution equations. Journal of Mathematical Analysis and Applications, 247(2), 627–644. https://doi.org/https://doi.org/10.1006/jmaa.2000.6896

Liu, J., Naito, T., & Van Minh, N. (2003). Bounded and periodic solutions of infinite delay evolution equations. Journal of Mathematical Analysis and Applications, 286(2), 705–712. https://doi.org/https://doi.org/10.1016/S0022-247X(03)00512-2

Lukes, D. L. (1972). Global Controllability of Nonlinear Systems. SIAM Journal on Control and Optimization, 10(1), 112–126. https://doi.org/https://doi.org/10.1137/0310011

Mirza, K. B., & Womack, B. F. (1972). On the Controllability of Nonlinear Time-Delay Systems. IEEE Transactions on Automatic Control, 17(6), 812–814. https://doi.org/https://doi.org/10.1109/TAC.1972.1100155

Nieto, J. J., & Tisdell, C. C. (2010). On exact controllability of first-order impulsive differential equations. Advances in Difference Equations, (136504). https://doi.org/https://doi.org/10.1155/2010/136504

Selvi, S., & Mallika, M. (2012). Controllability results for Impulsive Differential Systems with finite Delay. Journal of Nonlinear Science and Applications, 5(3), 206–219. https://doi.org/http://dx.doi.org/10.22436/jnsa.005.03.05

Sinha, A. S. C. (1985). Null-Controllability of Non-Linear Infinite Delay Systems with Restrained Controls. International Journal of Control, 42(3), 735–741. https://doi.org/https://doi.org/10.1080/00207178508933394

Sinha, A. S. C., & Yokomoto, C. F. (1980). Null Controllability of a Nonlinear System with Variable Time Delay. IEEE Transactions on Automatic Control, 25(6), 1234–1236. https://doi.org/https://doi.org/10.1109/TAC.1980.1102522

Smart, J. D. R. (1980). Fixed Point Theorems. In Methods of Mathematical Economics (pp. 224–292). Berlin, Heidelberg: Springer. https://doi.org/https://doi.org/10.1007/978-3-662-25317-5_3

Sontag, E. D. (1998). Mathematical Control Theory: Deterministic Finite Dimensional Systems (2nd ed.). NY USA: Springer. https://doi.org/https://doi.org/10.1007/978-1-4612-0577-7

Vidyasager, M. (1972). A Controllability Condition for Nonlinear Systems. IEEE Transactions on Automatic Control, 17(4), 569–570. https://doi.org/https://doi.org/10.1109/TAC.1972.1100064

Zhu, Z.-Q., & Lin, Q.-W. (2012). Exact Controllability of Semilinear Systems with Impulses. Bulletin of Mathematical Analysis and Applications, 4(1), 157–167. https://doi.org/https://www.emis.de/journals/BMAA/repository/docs/BMAA4_1_15.pdf

Publicado

2022-07-05

Cómo citar

Allauca, S., & Leiva, H. (2022). Controlabilidad de ecuaciones diferenciales retardadas semilineales impulsivas con retardo infinito y condiciones no locales. Novasinergia, ISSN 2631-2654, 5(2), 6–22. https://doi.org/10.37135/ns.01.10.01

Número

Sección

Artículos de Investigación y Artículos de Revisión