Table of Contents Author Guidelines Submit a Manuscript
Complexity
Volume 2017 (2017), Article ID 5308013, 11 pages
https://doi.org/10.1155/2017/5308013
Research Article

Calculus of Variations and Nonlinear Optimization Based Algorithm for Optimal Control of Hybrid Systems with Controlled Switching

1High Institute of Technological Studies in Communications (ISET’COM), Tunis, Tunisia
2Automatic Research Laboratory (LARA), National Engineering School of Tunis (ENIT), Tunis, Tunisia

Correspondence should be addressed to Hajer Bouzaouache

Received 10 February 2017; Revised 7 July 2017; Accepted 10 July 2017; Published 10 August 2017

Academic Editor: Michele Scarpiniti

Copyright © 2017 Hajer Bouzaouache. 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. D. Liberzon, “Finite data-rate feedback stabilization of switched and hybrid linear systems,” Automatica, vol. 50, no. 2, pp. 409–420, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  2. M. S. Shaikh and P. E. Caines, “On the Optimal Control of Hybrid Systems: Optimization of Trajectories, Switching Times, and Location Schedules,” in Hybrid Systems: Computation and Control, vol. 2623 of Lecture Notes in Computer Science, pp. 466–481, Springer, Berlin, Germany, 2003. View at Publisher · View at Google Scholar
  3. L. Hai, “Hybrid Dynamical Systems: An Introduction to Control and Verification,” Foundations and Trends® in Systems and Control, vol. 1, no. 1, pp. 1–172, 2014. View at Publisher · View at Google Scholar
  4. B. s. Temoçin and G.-W. Weber, “Optimal control of stochastic hybrid system with jumps: a numerical approximation,” Journal of Computational and Applied Mathematics, vol. 259, no. part B, pp. 443–451, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  5. N. Baleghi and M. Shafiei, “Stability analysis for discrete-time switched systems with uncertain time delay and affine parametric uncertainties,” Transactions of the Institute of Measurement and Control, 2016. View at Publisher · View at Google Scholar
  6. S. Hedlund and A. Rantzer, “Optimal control of hybrid systems,” in Proceedings of the The 38th IEEE Conference on Decision and Control (CDC), pp. 3972–3977, Phoenix, Ariz, USA, December 1999. View at Scopus
  7. J. Lunze and F. Lamnabhi-Lagarrigue, Eds., Handbook of Hybrid Systems Control, Cambridge University Press, Cambridge, UK, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  8. C. Liu and Z. Gong, Optimal control of switched systems arising in fermentation processes, vol. 97 of Springer Optimization and Its Applications, Springer, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  9. D. Görges, Optimal Control of Switched Systems with Application to Networked Embedded Control Systems, Logos Verlag Berlin GmbH, Berlin, Germany, 2012.
  10. N. B. H. Messaadi and H. Bouzaouache, “Sur la commande optimale des systèmes dynamiques hybrides autonomes: application à un processus chimique,” in Proceedings of the Conférence internationale JTEA206, Hammamet, Tunisia.
  11. T. J. Böhme and B. Frank, Hybrid Systems, Optimal Control and Hybrid Vehicles Theory, Methods and Applications, Springer International Publishing, 2017. View at Publisher · View at Google Scholar
  12. S. A. Attia, M. Alamir, and C. C. De Wit, “Sub optimal control of switched nonlinear systems under location and switching constraints,” in Proceedings of the 16th Triennial World Congress of International Federation of Automatic Control, IFAC 2005, pp. 133–138, cze, July 2005. View at Scopus
  13. X. Xu and P. J. Antsaklis, “Optimal control of switched systems via non-linear optimization based on direct differentiations of value functions,” International Journal of Control, vol. 75, no. 16-17, pp. 1406–1426, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. X. Xu and P. J. Antsaklis, “Optimal control of switched systems based on parameterization of the switching instants,” Institute of Electrical and Electronics Engineers. Transactions on Automatic Control, vol. 49, no. 1, pp. 2–16, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  15. X. Wu, K. Zhang, and C. Sun, “Constrained optimal control of switched systems and its application,” Optimization. A Journal of Mathematical Programming and Operations Research, vol. 64, no. 3, pp. 539–557, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. W. Zhang and J. Hu, “Optimal quadratic regulation for discrete-time switched linear systems: A numerical approach,” in Proceedings of the 2008 American Control Conference, ACC, pp. 4615–4620, usa, June 2008. View at Publisher · View at Google Scholar · View at Scopus
  17. M. Alamir and I. Balloul, “Robust constrained control algorithm for general batch processes,” International Journal of Control, vol. 72, no. 14, pp. 1271–1287, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. A. Bemporad, A. Giua, and C. Seatzu, “An iterative algorithm for the optimal control of continuous-time switched linear systems,” in Proceedings of the 6th International Workshop on Discrete Event Systems, WODES 2002, pp. 335–340, esp, October 2002. View at Publisher · View at Google Scholar · View at Scopus
  19. M. S. Branicky and S. K. Mitter, “Algorithms for optimal hybrid control,” in Proceedings of the 34th IEEE Conference on Decision and Control, 2000.
  20. A. E. Bryson and Y. C. Ho, Applied Optimal Control: Optimization, Estimation, and Control, Hemisphere, Washington, USA, 1975. View at MathSciNet
  21. R. V. Gamkrelidze, “Discovery of the maximum principle,” Journal of Dynamical and Control Systems, vol. 5, no. 4, pp. 437–451, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. H. Sussmann, “A maximum principle for hybrid optimal control problems,” in Proceedings of the 1999 Conference on Decision and Control, pp. 425–430, Phoenix, Ariz, USA. View at Publisher · View at Google Scholar
  23. A. Rantzer, “Dynamic programming via convex optimization,” IFAC Proceedings Volumes, vol. 32, no. 2, pp. 2059–2064, 1999. View at Publisher · View at Google Scholar
  24. D. Liberzon, Calculus of Variations and Optimal Control Theory, Princeton University Press, Princeton, NJ, USA, 2012. View at MathSciNet
  25. F. Zhu and P. J. Antsaklis, “Optimal control of hybrid switched systems: a brief survey,” Discrete Event Dynamic Systems: Theory and Applications, vol. 25, no. 3, pp. 345–364, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  26. J. D. Hoffman, “Numerical methods for engineers and scientists,” in Proceedings of the MC Graw-Hill International editions, Mechanical engineering series, New York, USA, 1993.
  27. M. S. Bazaraa and C. M. Shetty, Nonlinear Programming Theory and Algorithms, John Wiley & Sons, New York, NY, USA, 1979. View at MathSciNet
  28. J. Nocedal and S. J. Wright, Numerical Optimization, Springer, New York, NY, USA, 1999. View at MathSciNet