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Abstract and Applied Analysis
Volume 2014, Article ID 752854, 12 pages
http://dx.doi.org/10.1155/2014/752854
Research Article

A Simple Exact Penalty Function Method for Optimal Control Problem with Continuous Inequality Constraints

School of Mathematical Science, Heilongjiang University, Harbin 150080, China

Received 13 December 2013; Accepted 14 April 2014; Published 8 May 2014

Academic Editor: Gaston M. N’Guérékata

Copyright © 2014 Xiangyu Gao 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. Y. Sakawa and Y. Shindo, “Optimal control of container of container cranes,” Automatica, vol. 18, no. 3, pp. 257–266, 1982. View at Publisher · View at Google Scholar
  2. C. H. Jiang, Q. Lin, C. Yu, K. L. Teo, and G.-R. Duan, “An exact penalty method for free terminal time optimal control problem with continuous inequality constraints,” Journal of Optimization Theory and Applications, vol. 154, no. 1, pp. 30–53, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. X. L. Liu and G. R. Duan, “Nonlinear optimal control for the soft landing of lunar lander,” in Proceedings of the 1st International Symposium on Systems and Control in Aerospace and Astronautics, pp. 1382–1387, Harbin, China, January 2006. View at Scopus
  4. X. Y. Gao and K. L. Teo, “Fuel optimal control of nonlinear spacecraft rendezvous system with collision avoidance constraint,” submitted to IEEE Transactions on Automatic Control.
  5. C. Büskens and H. Maurer, “SQP-methods for solving optimal control problems with control and state constraints: adjoint variables, sensitivity analysis and real-time control,” Journal of Computational and Applied Mathematics, vol. 120, no. 1-2, pp. 85–108, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. W. Huyer and A. Neumaier, “A new exact penalty function,” SIAM Journal on Optimization, vol. 13, no. 4, pp. 1141–1158, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. T. W. Chen and V. S. Vassiliadis, “Inequality path constraints in optimal control: a finite iteration ε-convergent scheme based on pointwise discretization,” Journal of Process Control, vol. 15, no. 3, pp. 353–362, 2005. View at Publisher · View at Google Scholar · View at Scopus
  8. M. Gerdts, “Global convergence of a nonsmooth Newton method for control-state constrained optimal control problems,” SIAM Journal on Optimization, vol. 19, no. 1, pp. 326–350, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. M. Gerdts, “A nonsmooth Newton's method for control-state constrained optimal control problems,” Mathematics and Computers in Simulation, vol. 79, no. 4, pp. 925–936, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. J. Chen and M. Gerdts, “Numerical solution of control-state constrained optimal control problems with an inexact smoothing Newton method,” IMA Journal of Numerical Analysis, vol. 31, no. 4, pp. 1598–1624, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. K. L. Teo, L. S. Jennings, H. W. J. Lee, and V. Rehbock, “The control parameterization enhancing transform for constrained optimal control problems,” Journal of the Australian Mathematical Society B: Applied Mathematics, vol. 40, no. 3, pp. 314–335, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. K. L. Teo and L. S. Jennings, “Nonlinear optimal control problems with continuous state inequality constraints,” Journal of Optimization Theory and Applications, vol. 63, no. 1, pp. 1–22, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. R. C. Loxton, K. L. Teo, V. Rehbock, and K. F. C. Yiu, “Optimal control problems with a continuous inequality constraint on the state and the control,” Automatica, vol. 45, no. 10, pp. 2250–2257, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. M. Gerdts and M. Kunkel, “A nonsmooth Newton's method for discretized optimal control problems with state and control constraints,” Journal of Industrial and Management Optimization, vol. 4, no. 2, pp. 247–270, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. K. L. Teo, C. J. Goh, and K. H. Wong, A Unified Computational Approach to Optimal Control Problems, vol. 55, Longman, New York, NY, USA, 1991. View at MathSciNet
  16. B. Li, C. J. Yu, K. L. Teo, and G. R. Duan, “An exact penalty function method for continuous inequality constrained optimal control problem,” Journal of Optimization Theory and Applications, vol. 151, no. 2, pp. 260–291, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet