Controllability, observability and optimal control of continuous-time 2-D systems
Jank, Gerhard
International Journal of Applied Mathematics and Computer Science, Tome 12 (2002), p. 181-195 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

We consider linear 2-D systems of Fornasini-Marchesini type in the continuous-time case with non-constant coefficients. Using an explicit representation of the solutions by utilizing the Riemann-kernel of the equation under consideration, we obtain controllability and observability criteria in the case of the inhomogeneous equation, where control is obtained by choosing the inhomogeneity appropriately, but also for the homogeneous equation, where control is obtained by steering with Goursat data. The optimal control problem with a quadratic cost functional is also solved.

Publié le : 2002-01-01
EUDML-ID : urn:eudml:doc:207578 
@article{bwmeta1.element.bwnjournal-article-amcv12i2p181bwm,
     author = {Jank, Gerhard},
     title = {Controllability, observability and optimal control of continuous-time 2-D systems},
     journal = {International Journal of Applied Mathematics and Computer Science},
     volume = {12},
     year = {2002},
     pages = {181-195},
     zbl = {1014.93017},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv12i2p181bwm}
}

Jank, Gerhard. Controllability, observability and optimal control of continuous-time 2-D systems. International Journal of Applied Mathematics and Computer Science, Tome 12 (2002) pp. 181-195. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv12i2p181bwm/

[000] Arnol'd V.I. (1980): Gewohnliche Differentialgleichungen. -Berlin: Springer.

[001] Bergmann J., Burgmeier P. and Weiher P. (1989): Explicit controllability criteria for Goursat problems. - Optim., Vol. 20, No. 3, pp. 281-290. | Zbl 0673.93004

[002] Gantmacher F.R. (1986): Matrizentheorie. - Berlin: Springer.

[003] Gyurkovics E and Jank G. (2001): Instant controllability for Goursat problems. - Int. Rep., Cadernos de Matematica, Universidade de Aveiro, Portugal, CM01I-02. | Zbl 1003.93006

[004] Jain A.K. and Jain J.R. (1977): Partial differential equations and finite difference methods in image processing, Part I-Image Representation. - J. Optim. Theory Appl., Vol. 23, pp. 65-91. | Zbl 0341.60022

[005] Jain A.K. and Jain J.R. (1978): Partial differential equations and finite difference methods in image processing, Part II—Image Restoration. - I.E.E.E. Trans. Automat. Contr., Vol. 23, No. 5, pp. 817-833.

[006] Kaczorek T. (1995): Local controllability and minimum energy control of 2-D linear time invariant systems with variable coefficients. - Multidim. Syst. Signal Process., Vol. 6, pp. 69-75. | Zbl 0817.93031

[007] Kaczorek T. (1996): Local controllability and minimum energy controlof continuous 2-D linear time invariant systems. - Bull. Polish Acad. Sci. Tech. Sci., Vol. 44, No. 1, pp. 67-74. | Zbl 0884.93012

[008] Pulvirenti G. and Santagati G. (1975): Sulla controllabilita completa in luogu determinatu ed in luogu variabile por un processo di controllo con parametri distributi. - Boll. U.M.I., IV. Ser. 11, Fasc. 3, pp. 316-328. | Zbl 0319.93013

[009] Sontag E.D. (1998): Mathematical Control Theory. - New York: Springer. | Zbl 0945.93001

[010] Vekua I.N. (1967): New Methods for Solving Elliptic Equations. - Amsterdam: North-Holland. | Zbl 0146.34301

[011] Wolfersdorf v. L. (1978): Zum Maximum-Prinzip von Pontrjagin fur eine Klassepartieller Differentialgleichungssysteme 1. Ordnung. - ZAMM, Vol. 58, pp. 261-269. | Zbl 0386.49013