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Controllability, Observability and Optimal Control of Continuous-Time 2-D Systems

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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.
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autor
  • Lehrstuhl II für Mathematik, RWTH Aachen, D-52056 Aachen, Germany
Bibliografia
  • [1] Arnol’d V.I. (1980): Gewöhnliche Differentialgleichungen. - Berlin: Springer.
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  • [3] Gantmacher F.R. (1986): Matrizentheorie. - Berlin: Springer.
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  • [7] 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.
  • [8] Kaczorek T. (1996): Local controllability and minimum energy control of continuous 2-D linear time invariant systems. - Bull. Polish Acad. Sci. Tech. Sci., Vol. 44, No. 1, pp. 67-74.
  • [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.
  • [10] Sontag E.D. (1998): Mathematical Control Theory. - New York: Springer.
  • [11] Vekua I.N. (1967): New Methods for Solving Elliptic Equations. - Amsterdam: North-Holland.
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Bibliografia
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bwmeta1.element.baztech-article-BPZ1-0001-0017
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