Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2017, Article ID 3835616, 9 pages
https://doi.org/10.1155/2017/3835616
Research Article

Control of Chaos Using the Controller Identification Technique

Department of Mathematics and Statistics, Federal University of Pelotas, Campus Universitário, No. 354, 96010-900 Pelotas, RS, Brazil

Correspondence should be addressed to Alexandre Molter; rb.moc.oohay@retlom.erdnaxela

Received 10 July 2017; Revised 18 October 2017; Accepted 22 October 2017; Published 14 November 2017

Academic Editor: Jonathan N. Blakely

Copyright © 2017 Alexandre Molter and Fabricio B. Cabral. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. G. Safonov and T.-C. Tsao, “The unfalsified control concept: a direct path from experiment to controller,” Feedback Control, Nonlinear Systems, and Complexity, vol. 202, pp. 196–214, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  2. M. G. Safonov and T.-C. Tsao, “The unfalsified control concept and learning,” Institute of Electrical and Electronics Engineers Transactions on Automatic Control, vol. 42, no. 6, pp. 843–847, 1997. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. J. M. Krause and P. P. Khargonekar, “A comparison of classical stochastic estimation and deterministic robust estimation,” Institute of Electrical and Electronics Engineers Transactions on Automatic Control, vol. 37, no. 7, pp. 994–1000, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. K. Poolla, P. Khargonekar, A. Tikku, J. Krause, and K. Nagpal, “A time-domain approach to model validation,” Institute of Electrical and Electronics Engineers Transactions on Automatic Control, vol. 39, no. 5, pp. 951–959, 1994. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. R. S. Smith and J. C. Doyle, “Model validation: a connection between robust control and identification,” Institute of Electrical and Electronics Engineers Transactions on Automatic Control, vol. 37, no. 7, pp. 942–952, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. M. G. Safonov and F. B. Cabral, “Fitting controllers to data,” Systems & Control Letters, vol. 43, no. 4, pp. 299–308, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  7. M. G. Safonov, “Origins of robust control: Early history and future speculations,” in Proceedings of the 7th IFAC Symposium on Robust Control Design, ROCOND'12, pp. 1–8, June 2012. View at Publisher · View at Google Scholar · View at Scopus
  8. O. E. Rössler, “An equation for continuous chaos,” Physics Letters A, vol. 57, no. 5, pp. 397-398, 1976. View at Publisher · View at Google Scholar · View at Scopus
  9. M. E. Gilpin, “Spiral chaos in a predator-prey model,” The American Naturalist, vol. 113, no. 2, pp. 306–308, 1979. View at Publisher · View at Google Scholar · View at MathSciNet
  10. R. R. Vence, “Predation and resource partitioning in one predator—two prey model communications,” The American Naturalist, vol. 112, no. 987, pp. 797–813, 1978. View at Publisher · View at Google Scholar
  11. V. Volterra, Leçons sur la Théorie Mathematique de la Lutte pour la Vie. Gauthier-Villars, Paris, 1931.
  12. R. Barrio, M. A. Martínez, S. Serrano, and D. Wilczak, “When chaos meets hyperchaos: 4D Rössler model,” Physics Letters A, vol. 379, no. 38, pp. 2300–2305, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  13. M. Rafikov and J. M. Balthazar, “On control and synchronization in chaotic and hyperchaotic systems via linear feedback control,” Communications in Nonlinear Science and Numerical Simulation, vol. 13, no. 7, pp. 1246–1255, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. J. Sun and Y. Zhang, “Impulsive control of Rössler systems,” Physics Letters A, vol. 306, no. 5-6, pp. 306–312, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  15. A. El-Gohary and M. T. Yassen, “Optimal control and synchronization of Lotka-Volterra model,” Chaos, Solitons & Fractals, vol. 12, no. 11, pp. 2087–2093, 2001. View at Publisher · View at Google Scholar · View at Scopus
  16. A. Molter and M. Rafikov, “Nonlinear optimal control of population systems: applications in ecosystems,” Nonlinear Dynamics, vol. 76, no. 2, pp. 1141–1150, 2014. View at Publisher · View at Google Scholar · View at Scopus
  17. M. Rafikov, J. M. Balthazar, and H. F. von Bremen, “Mathematical modeling and control of population systems: applications in biological pest control,” Applied Mathematics and Computation, vol. 200, no. 2, pp. 557–573, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. H. T. Banks, B. M. Lewis, and H. T. Tran, “Nonlinear feedback controllers and compensators: A state-dependent Riccati equation approach,” Computational Optimization and Applications, vol. 37, no. 2, pp. 177–218, 2007. View at Publisher · View at Google Scholar · View at Scopus
  19. C. P. Mracek and J. R. Cloutier, “Control designs for the nonlinear benchmark problem via the state-dependent Riccati equation method,” International Journal of Robust and Nonlinear Control, vol. 8, no. 4-5, pp. 401–433, 1998. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. A. Molter and M. Rafikov, “Controle ótimo para um Sistema Caótico de Lotka-Volterra,” TEMA - Tendências em Matemática Aplicada e Computacional, vol. 5, no. 2, 2004. View at Publisher · View at Google Scholar