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2003 | 13 | 1 | 45-54
Tytuł artykułu

An application of the Fourier transform to optimization of continuous 2-D systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper uses the theory of entire functions to study the linear quadratic optimization problem for a class of continuous 2D systems. We show that in some cases optimal control can be given by an analytical formula. A simple method is also proposed to find an approximate solution with preassigned accuracy. Some application to the 1D optimization problem is presented, too. The obtained results form a theoretical background for the design problem of optimal controllers for relevant processes.
Rocznik
Tom
13
Numer
1
Strony
45-54
Opis fizyczny
Daty
wydano
2003
otrzymano
2002-09-01
poprawiono
2003-01-01
Twórcy
  • Graduate College, University of Erlangen-Nürnberg, Cauerstreet 7, D-91058, Erlangen, Germany
  • Institute of Mathematics, National Academy of Sciences, Surganov, 11, 220072, Minsk, Belarus
Bibliografia
  • Armand J.-L. (1977): Applications of Optimal Control Systems Theory. - Moscow: Nauka (in Russian).
  • Bose N.K. (1982): Applied Multidimensional System Theory. - New York: Van Nostrand Reinhold Company.
  • Chramtzov O. (1985): Controllability of stationary Pffaf differential equations. - Diff. Eqns., Vol. 21, No. 11, pp. 1933-1939.
  • Dymkov M.P. (1999): Quadratic optimization problems for two-dimensional (2-D) discrete continuous control systems. - Bull. Polish Acad. Sci., Techn.Sci., Vol. 47, No. 2, pp. 163-174.
  • Dymkov M. (2001): Entire function methods for optimization problems in continuous-discrete 2D control systems, In: Multidimensional Signal, Circuits and Systems(K. Gałkowski and J. Wood, Eds.). - London: Taylor and Francis, pp. 171-182.
  • Fornasini E. and Marchesini G. (1978): Doubly-indexed dynamical systems: State space models and structural properties. - Math. Syst. Theory, Vol. 12, No. 1, pp. 59-72.
  • Gaishun I.V. (1983): Complete Solvable Multidimensinal Differential Equations. - Minsk: Nauka and Tekhnika, (in Russian).
  • Gabasov R. and Kirillova F.M. (1988): Software Optimization. - USA: Plenum Press.
  • Ibragimov I. (1984): Advanced Theory of Analytic Functions. - Baku: Elm, (in Russian).
  • Idczak D. and Walczak S. (2000): On the existence of a solution for some distributed optimal control parabolic system. - Int. J. Math. Math. Sci., Vol. 23, No. 5, pp. 297-311.
  • Kaczorek T. (1985): Two Dimensional Linear Systems.- Berlin: Springer.
  • Kaczorek T. (1995): Generalized 2D continuous-discrete linear systems with delays. - Appl. Math. Comp. Scince, Vol. 5, No. 3, pp. 439-454.
  • Khurgin Ya.I. and Yakovlev V.P. (1971): Finite Functions in Physics and Technics. - Moscow: Nauka, (in Russian).
  • Perov K.A. (1975): Optimal Control for Problems of Mathematical Physics. - Moscow: Nauka, (in Russian).
  • Rashevski P.K. (1947): Geometric Theory of Partial Differential Equations. - Moscow: Nauka, (in Russian).
  • Shankar S. and Willems J. (2000): Behavioursof nD distributed systems. - Proc. 2nd Int. Workshops Multidimensional (nD) Systems, (NDS-2000), Zielona Góra, Poland, pp. 23-30.
  • Vasilyev F.P. (1981): Numerical Methods for Extremal Problems. - Moscow: Nauka, (in Russian).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv13i1p45bwm
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