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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 412509, 13 pages
http://dx.doi.org/10.1155/2013/412509
Research Article

Output Tracking Control of Switched Hybrid Systems: A Fliess Functional Expansion Approach

1Control and Simulation Center, Harbin Institute of Technology, Harbin, Heilongjiang 150080, China
2Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang 150080, China
3Harbin Institute of Technology, Harbin, Heilongjiang 150080, China
4Department of Mechanical Engineering, Harbin Institute of Technology, Harbin, Heilongjiang 150080, China

Received 5 April 2013; Accepted 18 May 2013

Academic Editor: Rongni Yang

Copyright © 2013 Fenghua He 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. J. A. Stiver and P. J. Antsaklis, “Modeling and analysis of hybrid control systems,” in Proceedings of the 31st IEEE Conference on Decision and Control, pp. 3748–3751, 1992.
  2. P. Antsaklis, X. Koutsoukos, and J. Zaytoon, “On hybrid control of complex systems: a survey,” Journal Europeen des Systemes Automatises, vol. 32, no. 9-10, pp. 1023–1045, 1998. View at Google Scholar · View at Scopus
  3. M. S. Branicky, V. S. Borkar, and S. K. Mitter, “A unified framework for hybrid control: model and optimal control theory,” IEEE Transactions on Automatic Control, vol. 43, no. 1, pp. 31–45, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. 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 Zentralblatt MATH · View at MathSciNet
  5. M. Lazar and W. P. M. H. Heemels, “Predictive control of hybrid systems: input-to-state stability results for sub-optimal solutions,” Automatica, vol. 45, no. 1, pp. 180–185, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. M. S. Shaikh and P. E. Caines, “On the hybrid optimal control problem: theory and algorithms,” IEEE Transactions on Automatic Control, vol. 52, no. 9, pp. 1587–1603, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  7. R. Goebel, R. G. Sanfelice, and A. R. Teel, “Hybrid dynamical systems: robust stability and control for systems that combine continuous-time and discrete-time dynamics,” IEEE Control Systems Magazine, vol. 29, no. 2, pp. 28–93, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  8. X. Xu and P. J. Antsaklis, “Optimal control of switched systems based on parameterization of the switching instants,” IEEE Transactions on Automatic Control, vol. 49, no. 1, pp. 2–16, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  9. L. Wu and J. Lam, “Sliding mode control of switched hybrid systems with time-varying delay,” International Journal of Adaptive Control and Signal Processing, vol. 22, no. 10, pp. 909–931, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. H. Lin and P. J. Antsaklis, “Stability and stabilizability of switched linear systems: a survey of recent results,” IEEE Transactions on Automatic Control, vol. 54, no. 2, pp. 308–322, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  11. L. Wu and W. X. Zheng, “Weighted H model reduction for linear switched systems with time-varying delay,” Automatica, vol. 45, no. 1, pp. 186–193, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. L. Wu, W. Zheng, and H. Gao, “Dissipativity-based sliding mode control of switched stochastic systems,” IEEE Transactions on Automatic Control, vol. 58, no. 3, pp. 785–793, 2013. View at Publisher · View at Google Scholar
  13. S. Ben Attia, S. Salhi, and M. Ksouri, “Static switched output feedback stabilization for linear discrete-time switched systems,” International Journal of Innovative Computing, Information and Control, vol. 8, no. 5, pp. 3203–3213, 2012. View at Google Scholar
  14. X. Su, P. Shi, L. Wu, and Y.-D. Song, “A novel control design on discrete-time takagi-sugeno fuzzy systems with time-varying delays,” IEEE Transactions on Fuzzy Systems, article 1, no. 99, 2012. View at Publisher · View at Google Scholar
  15. R. Yang, P. Shi, G.-P. Liu, and H. Gao, “Network-based feedback control for systems with mixed delays based on quantization and dropout compensation,” Automatica, vol. 47, no. 12, pp. 2805–2809, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. L. Wu, D. W. C. Ho, and C. W. Li, “Sliding mode control of switched hybrid systems with stochastic perturbation,” Systems & Control Letters, vol. 60, no. 8, pp. 531–539, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. H. Lin and P. J. Antsaklis, “Stability and stabilizability of switched linear systems: a survey of recent results,” IEEE Transactions on Automatic Control, vol. 54, no. 2, pp. 308–322, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  18. F. Zhu and P. J. Antsaklis, “Optimal control of switched hybrid systems: a brief survey,” Tech. Rep. ISIS-2011-003, 2011. View at Google Scholar
  19. F. Borrelli, M. Baotić, A. Bemporad, and M. Morari, “Dynamic programming for constrained optimal control of discrete-time linear hybrid systems,” Automatica, vol. 41, no. 10, pp. 1709–1721, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. D. Görges, M. Izák, and S. Liu, “Optimal control and scheduling of switched systems,” IEEE Transactions on Automatic Control, vol. 56, no. 1, pp. 135–140, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  21. 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
  22. X. Xu and P. J. Antsaklis, “Optimal control of switched autonomous systems,” in Proceedings of the 41st IEEE Conference on Decision and Control, vol. 4, pp. 4401–4406, December 2002. View at Scopus
  23. X. Xu and P. J. Antsaklis, “Results and perspectives on computational methods for optimal control of switched systems,” in Hybrid Systems: Computation and Control, pp. 540–555, Springer, Berlin, Germany, 2003. View at Google Scholar
  24. S. C. Bengea and R. A. DeCarlo, “Optimal control of switching systems,” Automatica, vol. 41, no. 1, pp. 11–27, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. S. Wei, K. Uthaichana, M. Žefran, 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 Zentralblatt MATH · View at MathSciNet
  26. T. Das and R. Mukherjee, “Optimally switched linear systems,” Automatica, vol. 44, no. 5, pp. 1437–1441, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  27. D. Nešić and L. Grüne, “Lyapunov-based continuous-time nonlinear controller redesign for sampled-data implementation,” Automatica, vol. 41, no. 7, pp. 1143–1156, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. L. Grüne and P. E. Kloeden, “Higher order numerical schemes for affinely controlled nonlinear systems,” Numerische Mathematik, vol. 89, no. 4, pp. 669–690, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. A. Isidori, Nonlinear Control Systems, Communications and Control Engineering Series, Springer, Berlin, Germany, 3rd edition, 1995. View at MathSciNet
  30. Y. Yao, B. Yang, F. He, Y. Qiao, and D. Cheng, “Attitude control of missile via fliess expansion,” IEEE Transactions on Control Systems Technology, vol. 16, no. 5, pp. 959–970, 2008. View at Publisher · View at Google Scholar · View at Scopus
  31. Y. Qiao, B. Yang, and D. Cheng, “Attitude control of missile via Fliess expansion and model predictive control,” in Proceedings of the 7th World Congress on Intelligent Control and Automation WCICA '08), pp. 1527–1532, June 2008. View at Publisher · View at Google Scholar · View at Scopus
  32. Y. Yao, B. Yang, F. He, and D. Cheng, “Fliess expansion-based bang-bang control design and its application to attitude control of missile,” in Proceedings of the 6th World Congress on Intelligent Control and Automation (WCICA '06), pp. 188–192, June 2006. View at Publisher · View at Google Scholar · View at Scopus
  33. P. Zarchan, Tactical and Strategic Missile Guidance, AIAA, San Diego, Calif, USA, 1997.
  34. Y. Yao, P. Zhang, H. H. T. Liu, and F. He, “Optimal sweep-based persistent surveillance using multiple unmanned aerial vehicles with level of interest,” in Proceedings of the 10th World Congress on Intelligent Control and Automation, pp. 2441–2446, Beijing, China, 2012.
  35. Y. Yao, P. Zhang, H. H. T. Liu, and F. He, “Optimal switching target-assignment based on the integral performance in cooperative tracking,” Science China Information Science, vol. 56, no. 1, pp. 1–14, 2013. View at Google Scholar