# 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

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topRachik, 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

top- 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.
- 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
- Athans M. and Falb P.L. (1996): Optimal Control. - New York: McGraw Hill.
- 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
- Lions J.L. (1988): Exact controllability, stabilization and perturbation for distributed systems. - SIAM J. Contr. Opt., Rev. 30, pp. 71-86.
- 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
- 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.
- Rachik M. (1995): Quelques elements sur l'analyse et le contrôle des systèmes distribues. - Ph. D. thesis, EMI-Rabat, Morocco.
- 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.
- 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
- 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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