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

• Autorzy: Gerhard Jank
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

2-D continuous-time systems; observability; optimal control; controllability; quadratic cost

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2002
• Tom: 12
• Numer: 2
• Strony: 181-195

Daty

wydano

2002

otrzymano

2000-12-18

poprawiono

2001-06-15

(nieznana)

2001-10-06

Twórcy

autor

Gerhard Jank

• Lehrstuhl II fur Mathematik, RWTH Aachen, D52056 Aachen, Germany

Bibliografia

• Arnol'd V.I. (1980): Gewohnliche Differentialgleichungen. -Berlin: Springer.
• Bergmann J., Burgmeier P. and Weiher P. (1989): Explicit controllability criteria for Goursat problems. - Optim., Vol. 20, No. 3, pp. 281-290.
• Gantmacher F.R. (1986): Matrizentheorie. - Berlin: Springer.
• Gyurkovics E and Jank G. (2001): Instant controllability for Goursat problems. - Int. Rep., Cadernos de Matematica, Universidade de Aveiro, Portugal, CM01I-02.
• 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.
• 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.
• 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.
• 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.
• 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.
• Sontag E.D. (1998): Mathematical Control Theory. - New York: Springer.
• Vekua I.N. (1967): New Methods for Solving Elliptic Equations. - Amsterdam: North-Holland.
• Wolfersdorf v. L. (1978): Zum Maximum-Prinzip von Pontrjagin fur eine Klassepartieller Differentialgleichungssysteme 1. Ordnung. - ZAMM, Vol. 58, pp. 261-269.