Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014, Article ID 268541, 9 pages
http://dx.doi.org/10.1155/2014/268541
Research Article

Optimal Control of Switching Topology Networks

1Department of Electrical and Electronics Engineering, National University of Colombia, Carrera 30, No. 45-03, Bogotá, Colombia
2Departamento de Ingeniería Eléctrica y Electrónica, Universidad de Los Andes, Carrera 1, No. 18A-12, Bogotá, Colombia
3Programa de Ingeniería Electrónica y Telecomunicaciones, Universidad Católica de Colombia, Avenida Caracas, No. 46-72, Bogotá, Colombia

Received 24 March 2014; Revised 20 June 2014; Accepted 21 June 2014; Published 7 July 2014

Academic Editor: Kh. S. Mekheimer

Copyright © 2014 Eduardo Mojica-Nava et al. 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. R. Olfati-Saber, J. A. Fax, and R. M. Murray, “Consensus and cooperation in networked multi-agent systems,” Proceedings of the IEEE, vol. 95, no. 1, pp. 215–233, 2007. View at Publisher · View at Google Scholar · View at Scopus
  2. E. Lovisari and S. Zampieri, “Performance metrics in the average consensus problem: a tutorial,” Annual Reviews in Control, vol. 36, no. 1, pp. 26–41, 2012. View at Publisher · View at Google Scholar · View at Scopus
  3. N. W. Bauer, P. J. H. Maas, and W. P. M. Heemels, “Stability analysis of networked control systems: a sum of squares approach,” Automatica, vol. 48, no. 8, pp. 1514–1524, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. E. Mojica-Nava, N. Quijano, and Rakoto-Ravalontsalama, “A polynomial approach for optimal control of switched nonlinear systems,” International Journal of Robust and Nonlinear Control, 2013. View at Publisher · View at Google Scholar
  5. A. Bemporad and M. Morari, “Control of systems integrating logic, dynamics, and constraints,” Automatica, vol. 35, no. 3, pp. 407–427, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. A. Bemporad, M. Morari, V. Dua, and E. N. Pistikopoulos, “The explicit solution of model predictive control via multiparametric quadratic programming,” in Proceedinhgs of the American Control Conference, vol. 2, pp. 872–876, Chicago, Ill, USA, June 2000. View at Publisher · View at Google Scholar · View at Scopus
  7. S. Wei, K. Uthaichana, M. Zefran, R. A. DeCarlo, and S. Bengea, “Applications of numerical optimal control to nonlinear hybrid systems,” Nonlinear Analysis: Hybrid Systems, vol. 1, no. 2, pp. 264–279, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. J. B. Lasserre, “Global optimization with polynomials and the problem of moments,” SIAM Journal on Optimization, vol. 11, no. 3, pp. 796–817, 2000/01. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. R. Meziat, “The method of moments in global optimization,” Journal of Mathematical Sciences, vol. 116, no. 3, pp. 3303–3324, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  10. J. B. Lasserre, “An explicit equivalent positive semidefinite program for nonlinear 0-1 programs,” SIAM Journal on Optimization, vol. 12, no. 3, pp. 756–769, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. J. B. Lasserre, “A semidefinite programming approach to the generalized problem of moments,” Mathematical Programming, vol. 112, no. 1, pp. 65–92, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. R. Meziat, D. Patiño, and P. Pedregal, “An alternative approach for non-linear optimal control problems based on the method of moments,” Computational Optimization and Applications, vol. 38, no. 1, pp. 147–171, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. P. Pedregal and J. Tiago, “Existence results for optimal control problems with some special nonlinear dependence on state and control,” SIAM Journal on Control and Optimization, vol. 48, no. 2, pp. 415–437, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  14. E. Mojica-Nava, N. Quijano, N. Rakoto-Ravalontsalama, and A. Gauthier, “A polynomial approach for stability analysis of switched systems,” Systems & Control Letters, vol. 59, no. 2, pp. 98–104, 2010. View at Publisher · View at Google Scholar · View at Scopus
  15. R. Burden and J. D. Faires, Numerical Analysis, PWS, Boston, Mass, USA, 1985.
  16. E. Mojica Nava, R. Meziat, N. Quijano, A. Gauthier, and N. Rakoto-Ravalontsalama, “Optimal control of switched systems: a polynomial approach,” in Proceedings of the 17th World Congress, International Federation of Automatic Control (IFAC '08), pp. 7808–7813, July 2008. View at Publisher · View at Google Scholar · View at Scopus
  17. R. E. Curto and L. A. Fialkow, “The truncated complex K-moment problem,” Transactions of the American Mathematical Society, vol. 352, no. 6, pp. 2825–2855, 2000. View at Publisher · View at Google Scholar · View at Scopus
  18. D. P. Bertsekas, Nonlinear Programming, Athena Scientific, Belmont, Mass, USA, 2nd edition, 1999.
  19. S. Sager, “Reformulations and algorithms for the optimization of switching decisions in nonlinear optimal control,” Journal of Process Control, vol. 19, no. 8, pp. 1238–1247, 2009. View at Publisher · View at Google Scholar · View at Scopus
  20. “Detecting global optimality and extracting solutions in GloptiPoly,” in Positive Polynomials in Control, D. Henrion and J. Lasserre, Eds., vol. 312 of Lecture Notes in Control and Information Sciences, pp. 293–310, Springer, Berlin, Germany, 2005. View at MathSciNet · View at Scopus
  21. Z. Sun and S. S. Ge, “Analysis and synthesis of switched linear control systems,” Automatica, vol. 41, no. 2, pp. 181–195, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus