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AN EFFICIENT ALGORITHM FOR FINDING OPTIMAL CAR-DRIVING STRATEGY

  • Farhadinia, Bahram (Department of Mathematics, Quchan Institute of Engineering and Technology)
  • Received : 2011.02.10
  • Accepted : 2011.07.04
  • Published : 2012.01.30

Abstract

In this paper, the problem of determining the optimal car-deriving strategy has been examined. In order to find the optimal driving strategy, we have modified a method based on measure theory. Further, we demonstrate that the modified method is an efficient and practical algorithm for dealing with optimal control problems in a canonical formulation.

Keywords

References

  1. M. H. Farahi, J. E. Rubio and D. A. Wilson, The optimal control of the linear wave equation, Int. J. of Control, 63, (1996), 833-848. https://doi.org/10.1080/00207179608921871
  2. B. Farhadinia, Shape optimization of an airfoil in the presence of compressible and viscus flows, Comput. Optim. Appl., DOI 10.1007/s10589-009-9313-y.
  3. B. Farhadinia and M. H. Farahi, Optimal shape design of an almost straight nozzle, Int. J. of Appl. Math., 17, (2005), 319-333.
  4. B. Farhadinia , M. H. Farahi and J. A. Esfahani, Shape optimization of a nozzle with specified fiow field including viscosity effect, Acta Appl. Math., 104, (2008), 243-256. https://doi.org/10.1007/s10440-008-9253-z
  5. B. Farhadinia , K. L. Teo and R. C. Loxton, A computational method for a class of non-standard time optimal control problems involving multiple time horizons, Math. Comput. Modeling, 49, (2009), 1682-1691. https://doi.org/10.1016/j.mcm.2008.08.019
  6. M. Gachpazan , A. H. Borzabadi and A. V. Kamyad, A measure-theoretical approach for solving discrete optimal control problems, Appl. Math. Comput., 173, (2006), 736-752.
  7. D. J. Gates and M. Westcott, Solar cars and variational problems equivalent to shortest paths, SIAM. J. Control and Optim., 34, (1996), 428-436. https://doi.org/10.1137/S0363012993260276
  8. B. Z. Guo and B. Sun, A new algorithm for finding numerical solutions of optimal feedback control , IMA J. Mathematical Control and Information, 26, (2009), 95-104.
  9. H. W. J. Lee, K. L. Teo, V. Rehbock and L. S. Jennings, Control parametrization enhancing technique and simulation on the design of a flexible rotating beam, J. Optim. Theory Appl., 136, (2008), 247-259. https://doi.org/10.1007/s10957-007-9303-0
  10. H. W. J. Lee, K. L. Teo, V. Rehbock and L. S. Jennings, Control parametrization enhancing technique for optimal discrete-valued control problems, Automatica 35, (1999), 1401-1407. https://doi.org/10.1016/S0005-1098(99)00050-3
  11. 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, 45, (2009), 2250-2257. https://doi.org/10.1016/j.automatica.2009.05.029
  12. J. E. Rubio, Control and optimization: the linear treatment of nonlinear problems, Manchester University Press, Manchester, and John Wiely, New York and London, 1986.
  13. J. E. Rubio, The global control of nonlinear diffusion equations, SIAM J. Control and Optimization, 33, (1995), 308-322. https://doi.org/10.1137/S0363012991222887
  14. W. Rudin, Real and complex analysis, 3rd Edn., New York, MC Graw Hill, 1987.
  15. K. L. Teo, L. S. Jennings, H. W. J. Lee and V. Rehbock, The control parametrization enhancing transform for constrained optimal control problems, J. Austral. Math. Soc. Ser. B 40, (1999), 314-335. https://doi.org/10.1017/S0334270000010936
  16. K. L. Teo, C. L. Goh and K. H.Wong, A unified computational approach to optimal control problems, Longman Scientific and Technical, London 1991.
  17. B. Vexler and W. Wollner, Adaptive finite elements for elliptic optimization problems with control constraints, SIAM J. Control Optim., 47, (2008), 509-534. https://doi.org/10.1137/070683416