Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 4829195, 10 pages
https://doi.org/10.1155/2017/4829195
Research Article

An Improved Finite Element Meshing Strategy for Dynamic Optimization Problems

School of Automation, Hangzhou Dianzi University, Hangzhou 310018, China

Correspondence should be addressed to Aipeng Jiang; moc.361@gnepiagnaij

Received 7 April 2017; Accepted 11 June 2017; Published 19 July 2017

Academic Editor: Rahmat Ellahi

Copyright © 2017 Minliang Gong 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. T. Betts and I. Kolmanovsky, Practical methods for optimal control using nonlinear programming [M.S. thesis], Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, USA, 2001.
  2. X. Liu, Y. Hu, J. Feng, and K. Liu, “A novel penalty approach for nonlinear dynamic optimization problems with inequality path constraints,” Institute of Electrical and Electronics Engineers. Transactions on Automatic Control, vol. 59, no. 10, pp. 2863–2867, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. L. T. Paiva and F. A. C. C. Fontes, “Time—mesh Refinement in Optimal Control Problems for Nonholonomic Vehicles,” Procedia Technology, vol. 17, pp. 178–185, 2014. View at Publisher · View at Google Scholar
  4. Y. Zhao and P. Tsiotras, “Density functions for mesh refinement in numerical optimal control,” Journal of Guidance, Control, and Dynamics, vol. 34, no. 1, pp. 271–277, 2011. View at Publisher · View at Google Scholar · View at Scopus
  5. H.-G. Li, J.-P. Liu, and J.-W. Huang, “Self-adaptive variable-step approach for iterative dynamic programming with applications in batch process optimization,” Control and Decision, vol. 30, no. 11, pp. 2048–2054, 2015. View at Publisher · View at Google Scholar · View at Scopus
  6. Z. Zhang, Y. Liao, and Y. Wen, “An adaptive variable step-size RKF method and its application in satellite orbit prediction,” Computer Engineering and Science, vol. 37, no. 4, pp. 842–846, 2015. View at Google Scholar
  7. P. Liu, G. Li, X. Liu, and Z. Zhang, “Novel non-uniform adaptive grid refinement control parameterization approach for biochemical processes optimization,” Biochemical Engineering Journal, vol. 111, pp. 63–74, 2016. View at Publisher · View at Google Scholar · View at Scopus
  8. L. Wang, X. Liu, and Z. Zhang, “A new sensitivity-based adaptive control vector parameterization approach for dynamic optimization of bioprocesses,” Bioprocess and Biosystems Engineering, vol. 40, no. 2, pp. 181–189, 2017. View at Google Scholar
  9. L. T. Biegler, Nonlinear programming: concepts, algorithms, and applications to chemical processes [M.S. thesis], Society for Industrial and Applied Mathematics, Pittsburgh, Pa, USA, 2010.
  10. W. F. Chen, K. X. Wang, Z. J. Shao, and L. T. Biegler, “Moving finite elements for dynamic optimization with direct transcription formulations,” in Control and Optimization with Differential-Algebraic Constraints, L. T. Biegler, S. L. Campbell, and V. Mehrmann, Eds., SIAM, Philadelphia, PA, USA, 2011. View at Google Scholar
  11. P. Tanartkit and L. T. Biegler, “A nested, simultaneous approach for dynamic optimization problems—II: the outer problem,” Computers and Chemical Engineering, vol. 21, no. 12, pp. 735–741, 1997. View at Google Scholar
  12. G. A. Hicks and W. H. Ray, “Approximation methods for optimal control synthesis,” The Canadian Journal of Chemical Engineering, vol. 49, no. 4, pp. 522–528, 1971. View at Publisher · View at Google Scholar
  13. J. S. Logsdon and L. T. Biegler, “Accurate solution of differential-algebraic optimization problems,” Industrial and Engineering Chemistry Research, vol. 28, no. 11, pp. 1628–1639, 1989. View at Publisher · View at Google Scholar · View at Scopus
  14. V. M. Zavala, Computational strategies for the optimal operation of large-scale chemical processes [Ph.D. thesis], Carnegie Mellon University, Pennsylvania, Pa, USA, 2008.
  15. J. Bausa, “Dynamic optimization of startup and load-increasing processes in power plants—part I: method,” Journal of Engineering for Gas Turbines and Power, vol. 123, no. 1, pp. 251–254, 2001. View at Google Scholar
  16. S. Vasantharajan and L. T. Biegler, “Simultaneous strategies for optimization of differential-algebraic systems with enforcement of error criteria,” Computers and Chemical Engineering, vol. 14, no. 10, pp. 1083–1100, 1990. View at Publisher · View at Google Scholar · View at Scopus
  17. A. Wächter and L. T. Biegler, “Line search filter methods for nonlinear programming: motivation and global convergence,” SIAM Journal on Optimization, vol. 16, no. 1, pp. 1–31, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  18. A. Chter and L. T. Biegler, “Line search filter methods for nonlinear programming: local convergence,” SIAM Journal on Optimization, vol. 16, no. 1, pp. 32–48, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  19. L. I. Qianxing, X. Liu, and W. U. Gaohui, “An adaptive step-size approach to iterative dynamic programming,” Bulletin of Science and Technology, vol. 26, no. 5, pp. 666–669, 2010. View at Google Scholar