Optimizing the linear quadratic minimum-time problem for discrete distributed systems

Mostafa Rachik; Ahmed Abdelhak

International Journal of Applied Mathematics and Computer Science (2002)

  • Volume: 12, Issue: 2, page 153-160
  • ISSN: 1641-876X

Abstract

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With reference to the work of Verriest and Lewis (1991) on continuous finite-dimensional systems, the linear quadratic minimum-time problem is considered for discrete distributed systems and discrete distributed time delay systems. We treat the problem in two variants, with fixed and free end points. We consider a cost functional J which includes time, energy and precision terms, and then we investigate the optimal pair (N, u) which minimizes J.

How to cite

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Rachik, Mostafa, and Abdelhak, Ahmed. "Optimizing the linear quadratic minimum-time problem for discrete distributed systems." International Journal of Applied Mathematics and Computer Science 12.2 (2002): 153-160. <http://eudml.org/doc/207575>.

@article{Rachik2002,
abstract = {With reference to the work of Verriest and Lewis (1991) on continuous finite-dimensional systems, the linear quadratic minimum-time problem is considered for discrete distributed systems and discrete distributed time delay systems. We treat the problem in two variants, with fixed and free end points. We consider a cost functional J which includes time, energy and precision terms, and then we investigate the optimal pair (N, u) which minimizes J.},
author = {Rachik, Mostafa, Abdelhak, Ahmed},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {time delay systems; minimum time; optimal control; discrete distributed systems; quadratic minimum-time problem; discrete distributed time delay system; free end points; existence and uniqueness},
language = {eng},
number = {2},
pages = {153-160},
title = {Optimizing the linear quadratic minimum-time problem for discrete distributed systems},
url = {http://eudml.org/doc/207575},
volume = {12},
year = {2002},
}

TY - JOUR
AU - Rachik, Mostafa
AU - Abdelhak, Ahmed
TI - Optimizing the linear quadratic minimum-time problem for discrete distributed systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2002
VL - 12
IS - 2
SP - 153
EP - 160
AB - With reference to the work of Verriest and Lewis (1991) on continuous finite-dimensional systems, the linear quadratic minimum-time problem is considered for discrete distributed systems and discrete distributed time delay systems. We treat the problem in two variants, with fixed and free end points. We consider a cost functional J which includes time, energy and precision terms, and then we investigate the optimal pair (N, u) which minimizes J.
LA - eng
KW - time delay systems; minimum time; optimal control; discrete distributed systems; quadratic minimum-time problem; discrete distributed time delay system; free end points; existence and uniqueness
UR - http://eudml.org/doc/207575
ER -

References

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  1. Abdelhak A. (1997): Quelques elements sur l'analyse et le contrôle des systèmes discrets à retard. - Ph. D. thesis, Faculte des Sciences Ben M'Sik, Casablanca, Morocco. 
  2. El Alami N., Ounsafi A. and Znaidi N. (1998): On the discrete linear quadratic minimum-time problem. - J. Franklin Institute, Vol. 335(b), pp. 525-532. Zbl0909.49018
  3. Athans M. and Falb P.L. (1996): Optimal Control. - New York: McGraw Hill. 
  4. Karrakchou J. and Rachik M. (1995): Optimal control of discrete distributed systems with delays in the control: The finite horizon case.- Arch. Contr. Sci., Vol. 4(XL), Nos. 1-2, pp. 37-53. Zbl0859.49005
  5. Lions J.L. (1988): Exact controllability, stabilization and perturbation for distributed systems. - SIAM J. Contr. Opt., Rev. 30, pp. 71-86. 
  6. Lee K.Y., Chown S.N. and Barr R.O. (1972): On the control of discrete time distributed parameter systems. - SIAM J. Contr., Vol. 10, No. 2, pp. 361-376. Zbl0253.49004
  7. Pohjolainen S. (1982): On the discrete-time quadratic optimum control problem in reflexive Banach space. - Proc. 2nd IFAC Symp., Coventry, Great Britain, Pergamon Press, pp. 319-328. 
  8. Rachik M. (1995): Quelques elements sur l'analyse et le contrôle des systèmes distribues. - Ph. D. thesis, EMI-Rabat, Morocco. 
  9. Schwartz H.M. and Gourdeau R. (1989): Optimal control of a robot manipulator using a weigthed time-energy cost function. - Proc. IEEEConf. Decision Contr., pp. 1628-1631. 
  10. Verriest E.I. and Lewis F.L. (1991): On the linear quadratic minimum-time problem. - IEEE Trans. Automat. Contr., Vol. 36, No. 7, pp. 859-863. Zbl0752.93036
  11. Zabczyk J. (1974): Remarks on the control of discrete-time parameter systems. - SIAM J. Contr., Vol. 12, No. 4, pp. 721-735. Zbl0254.93027

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