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

• Autorzy: Mostafa Rachik , Ahmed Abdelhak
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

time delay systems; minimum time; optimal control; discrete distributed systems

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2002
• Tom: 12
• Numer: 2
• Strony: 153-160

Daty

wydano

2002

otrzymano

2000-05-25

poprawiono

2001-06-18

Twórcy

autor

Mostafa Rachik

• Faculté des Sciences Ben M'Sik, Département de Mathématiques Université Hassan II Mohammadia, Casablanca, Morocco

autor

Ahmed Abdelhak

• Faculté des Sciences Ben M'Sik, Département de Mathématiques Université Hassan II Mohammadia, Casablanca, Morocco

Bibliografia

• 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.
• 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.
• 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.
• 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.
• Zabczyk J. (1974): Remarks on the control of discrete-time parameter systems. - SIAM J. Contr., Vol. 12, No. 4, pp. 721-735.