AN EVOLUTIONARY APPROACH TO NONLINEAR DISCRETE-TIME OPTIMAL CONTROL WITH TERMINAL CONSTRAINTS

Yechiel Crispin

2004

Abstract

The nonlinear discrete-time optimal control problem with terminal constraints is treated using a new evolutionary approach which combines a genetic search for finding the control sequence with a solution of the initial value problem for the state variables. The main advantage of the method is that it does not require to obtain the solution of the adjoint problem which usually leads to a two-point boundary value problem combined with an optimality condition for finding the control sequence. The method is verified by solving the problem of discrete velocity direction programming with the effects of gravity and thrust and a terminal constraint on the final vertical position. The solution compared favorably with the results of gradient methods.

References

  1. Bryson, A. E. and Ho, Y. C., Applied Optimal Control, Hemisphere, Washington, D.C., 1975.
  2. Bryson, A.E., Dynamic Optimization, Addison-Wesley Longman, Menlo Park, CA, 1999.
  3. Coleman, T.F. and Liao, A., An efficient trust region method for unconstrained discrete-time optimal control problems, Computational Optimization and Applications, 4, pp. 47-66, 1995.
  4. Dunn, J., and Bertsekas, D.P., Efficient dynamic programming implementations of Newton's method for unconstrained optimal control problems, J. of Optimization Theory and Applications, 63 (1989), pp. 23-38.
  5. Fogel, D.B., Evolutionary Computation, The Fossil Record, IEEE Press, New York, 1998.
  6. Fox, C., An Introduction to the Calculus of Variations, Oxford University Press, London, 1950.
  7. Jacobson, D. and Mayne, D. , Differential Dynamic Programming, Elsevier Science Publishers, 1970.
  8. Kirkpatrick, and Gelatt, C.D. and Vecchi, Optimization by Simulated Annealing, Science, 220, 671-680, 1983.
  9. Laarhoven, P.J.M. and Aarts, E.H.L., Simulated Annealing: Theory and Applications, Kluwer Academic, 1989.
  10. Liao, L.Z. and Shoemaker, C.A., Convergence in unconstrained discrete-time differential dynamic programming, IEEE Trans. Automat. Contr., 36, pp. 692-706, 1991.
  11. Mayne, D., A second-order gradient method for determining optimal trajectories of non-linear discrete time systems, Intnl. J. Control, 3 (1966), pp. 85-95.
  12. Michalewicz, Z., Genetic Algorithms + Data Structures = Evolution Programs, Springer-Verlag, Berlin, 1992a.
  13. Michalewicz, Z., Janikow, C.Z. and Krawczyk, J.B., A Modified Genetic Algorithm for Optimal Control Problems, Computers Math. Applications, 23(12), pp. 83-94, 1992b.
  14. Murray, D.M. and Yakowitz, S.J., Differential dynamic programming and Newton's method for discrete optimal control problems, J. of Optimization Theory and Applications, 43, pp. 395-414, 1984.
  15. Ohno, K., A new approach of differential dynamic programming for discrete time systems, IEEE Trans. Automat. Contr., 23 (1978), pp. 37-47.
  16. Pantoja, J.F.A. de O. , Differential Dynamic Programming and Newton's Method, International Journal of Control, 53: 1539-1553, 1988.
  17. Pontryagin, L. S. Boltyanskii, V. G., Gamkrelidze, R. V. and Mishchenko, E. F., The Mathematical Theory of Optimal Processes, Moscow, 1961, translated by Trirogoff, K. N. Neustadt, L. W. (Ed.), Interscience, New York, 1962.
  18. Schwefel H.P., Evolution and Optimum Seeking, Wiley, New York, 1995.
  19. Yakowitz, S.J., and Rutherford, B., Computational aspects of discrete-time optimal control, Appl. Math. Comput., 15 (1984), pp. 29-45.
Download


Paper Citation


in Harvard Style

Crispin Y. (2004). AN EVOLUTIONARY APPROACH TO NONLINEAR DISCRETE-TIME OPTIMAL CONTROL WITH TERMINAL CONSTRAINTS . In Proceedings of the First International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 972-8865-12-0, pages 49-57. DOI: 10.5220/0001134700490057


in Bibtex Style

@conference{icinco04,
author={Yechiel Crispin},
title={AN EVOLUTIONARY APPROACH TO NONLINEAR DISCRETE-TIME OPTIMAL CONTROL WITH TERMINAL CONSTRAINTS},
booktitle={Proceedings of the First International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2004},
pages={49-57},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001134700490057},
isbn={972-8865-12-0},
}


in EndNote Style

TY - CONF
JO - Proceedings of the First International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
TI - AN EVOLUTIONARY APPROACH TO NONLINEAR DISCRETE-TIME OPTIMAL CONTROL WITH TERMINAL CONSTRAINTS
SN - 972-8865-12-0
AU - Crispin Y.
PY - 2004
SP - 49
EP - 57
DO - 10.5220/0001134700490057