Controllability, observability and optimal control of continuous-time 2-D systems

Gerhard Jank

International Journal of Applied Mathematics and Computer Science (2002)

  • Volume: 12, Issue: 2, page 181-195
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Jank, Gerhard. "Controllability, observability and optimal control of continuous-time 2-D systems." International Journal of Applied Mathematics and Computer Science 12.2 (2002): 181-195. <http://eudml.org/doc/207578>.

@article{Jank2002,
abstract = {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.},
author = {Jank, Gerhard},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {2-D continuous-time systems; observability; optimal control; controllability; quadratic cost; 2-D linear systems; linear hyperbolic system; Goursat conditions; Riemann kernel function; integral equation of Volterra type},
language = {eng},
number = {2},
pages = {181-195},
title = {Controllability, observability and optimal control of continuous-time 2-D systems},
url = {http://eudml.org/doc/207578},
volume = {12},
year = {2002},
}

TY - JOUR
AU - Jank, Gerhard
TI - Controllability, observability and optimal control of continuous-time 2-D systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2002
VL - 12
IS - 2
SP - 181
EP - 195
AB - 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.
LA - eng
KW - 2-D continuous-time systems; observability; optimal control; controllability; quadratic cost; 2-D linear systems; linear hyperbolic system; Goursat conditions; Riemann kernel function; integral equation of Volterra type
UR - http://eudml.org/doc/207578
ER -

References

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  8. 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. Zbl0884.93012
  9. 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. Zbl0319.93013
  10. Sontag E.D. (1998): Mathematical Control Theory. - New York: Springer. Zbl0945.93001
  11. Vekua I.N. (1967): New Methods for Solving Elliptic Equations. - Amsterdam: North-Holland. Zbl0146.34301
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