Table of Contents Author Guidelines Submit a Manuscript
Differential Equations and Nonlinear Mechanics
Volume 2007, Article ID 18735, 16 pages
http://dx.doi.org/10.1155/2007/18735
Research Article

Optimal Control of Mechanical Systems

Departamento de Control Automatico, CINVESTAV, Av. Instituto Politecnico Nacional 2508, Col. San Pedro Zacatenco, Mexico 07360, DF, Mexico

Received 7 February 2007; Accepted 10 May 2007

Academic Editor: John R. Cannon

Copyright © 2007 Vadim Azhmyakov. 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. Baillieul, “The geometry of controlled mechanical systems,” in Mathematical Control Theory, J. Baillieul and J. C. Willems, Eds., pp. 322–354, Springer, New York, NY, USA, 1999. View at Zentralblatt MATH · View at MathSciNet
  2. A. M. Bloch and P. E. Crouch, “Optimal control, optimization, and analytical mechanics,” in Mathematical Control Theory, J. Baillieul and J. C. Willems, Eds., pp. 268–321, Springer, New York, NY, USA, 1999. View at Zentralblatt MATH · View at MathSciNet
  3. R. W. Brockett, “Control theory and analytical mechanics,” in Conference on Geometric Control Theory (Moffett Field, Calif, 1976), C. F. Martin and R. Hermann, Eds., pp. 1–48, Math. Sci. Press, Brookline, Mass, USA, 1977. View at Zentralblatt MATH · View at MathSciNet
  4. H. Nijmeijer and A. van der Schaft, “Nonlinear Dynamical Control Systems,” Springer, New York, NY, USA, 1990. View at Zentralblatt MATH · View at MathSciNet
  5. V. Azhmyakov, “A numerically stable method for convex optimal control problems,” Journal of Nonlinear and Convex Analysis, vol. 5, no. 1, pp. 1–18, 2004. View at Zentralblatt MATH · View at MathSciNet
  6. V. Azhmyakov and W. Schmidt, “Approximations of relaxed optimal control problems,” Journal of Optimization Theory and Applications, vol. 130, no. 1, pp. 61–78, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  7. E. Polak, Optimization, vol. 124 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1997. View at Zentralblatt MATH · View at MathSciNet
  8. R. Pytlak, Numerical Methods for Optimal Control Problems with State Constraints, vol. 1707 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1999. View at Zentralblatt MATH · View at MathSciNet
  9. K. L. Teo, C. J. Goh, and K. H. Wong, A Unified Computational Approach to Optimal Control Problems, vol. 55 of Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman Scientific & Technical, Harlow, UK; John Wiley & Sons, New York, NY, USA, 1991. View at Zentralblatt MATH · View at MathSciNet
  10. R. E. Bellman and S. E. Dreyfus, “Applied Dynamic Programming,” Princeton University Press, Princeton, NJ, USA, 1962. View at Zentralblatt MATH · View at MathSciNet
  11. A. E. Bryson Jr. and Y. C. Ho, “Applied Optimal Control,” John Wiley & Sons, New York, NY, USA, 1975. View at MathSciNet
  12. J. F. Bonnans, “On an algorithm for optimal control using Pontryagin's maximum principle,” SIAM Journal on Control and Optimization, vol. 24, no. 3, pp. 579–588, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Y. Sakawa, Y. Shindo, and Y. Hashimoto, “Optimal control of a rotary crane,” Journal of Optimization Theory and Applications, vol. 35, no. 4, pp. 535–557, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. S. J. Wright, “Interior point methods for optimal control of discrete time systems,” Journal of Optimization Theory and Applications, vol. 77, no. 1, pp. 161–187, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. M. Fukushima and Y. Yamamoto, “A second-order algorithm for continuous-time nonlinear optimal control problems,” IEEE Transactions on Automatic Control, vol. 31, no. 7, pp. 673–676, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. 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 Zentralblatt MATH · View at MathSciNet
  17. F.-S. Kupfer and E. W. Sachs, “Reduced SQP methods for nonlinear heat conduction control problems,” in Optimal Control (Freiburg, 1991), vol. 111 of International Series of Numerical Mathematics, pp. 145–160, Birkhäuser, Basel, Switzerland, 1993. View at Zentralblatt MATH · View at MathSciNet
  18. R. Abraham, Foundations of Mechanics, W. A. Benjamin, New York, NY, USA, 1967. View at Zentralblatt MATH
  19. V. I. Arnold, “Mathematical Methods of Classical Mechanics,” Springer, New York, NY, USA, 1978. View at Zentralblatt MATH · View at MathSciNet
  20. A. D. Ioffe and V. M. Tihomirov, Theory of Extremal Problems, vol. 6 of Studies in Mathematics and Its Applications, North-Holland, Amsterdam, The Netherlands, 1979. View at Zentralblatt MATH · View at MathSciNet
  21. F. R. Gantmakher, Lectures on Analytical Mechanics, Nauka, Moscow, Russia, 1966.
  22. J. C. Dunn, “On state constraint representations and mesh-dependent gradient projection convergence rates for optimal control problems,” SIAM Journal on Control and Optimization, vol. 39, no. 4, pp. 1082–1111, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. R. Fletcher, Practical Methods of Optimization, John Wiley & Sons, New York, NY, USA, 1991.
  24. Y. Sawaragi, H. Nakayama, and T. Tanino, Theory of Multiobjective Optimization, vol. 176 of Mathematics in Science and Engineering, Academic Press, Orlando, Fla, USA, 1985. View at Zentralblatt MATH · View at MathSciNet
  25. F. H. Clarke, Optimization and Nonsmooth Analysis, vol. 5 of Classics in Applied Mathematics, SIAM, Philadelphia, Pa, USA, 2nd edition, 1990. View at Zentralblatt MATH · View at MathSciNet
  26. V. Azhmyakov, “On optimal control of mechanical systems,” Tech. Rep. 22, EMA University of Greifswald, Greifswald, Germany, 2003.