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Języki publikacji
Abstrakty
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
Strony
45--54
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
autor
- Graduate College, University of Erlangen-Nürnberg, Cauerstreet 7, D–91058, Erlangen, Germany
autor
- Institute of Mathematics, National Academy of Sciences, Surganov, 11, 220072, Minsk, Belarus
Bibliografia
- [1] Armand J.-L. (1977): Applications of Optimal Control Systems Theory. — Moscow: Nauka (in Russian).
- [2] Bose N.K. (1982): Applied Multidimensional System Theory.— New York: Van Nostrand Reinhold Company.
- [3] Chramtzov O. (1985): Controllability of stationary Pffaf differential equations.—Diff. Eqns., Vol. 21, No. 11, pp. 1933–1939.
- [4] 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.
- [5] 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.
- [6] 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.
- [7] Gaishun I.V. (1983): Complete Solvable Multidimensinal Differential Equations. — Minsk: Nauka and Tekhnika, (in Russian).
- [8] Gabasov R. and Kirillova F.M. (1988): Software Optimization. —USA: Plenum Press.
- [9] Ibragimov I. (1984): Advanced Theory of Analytic Functions.— Baku: Elm, (in Russian).
- [10] 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.
- [11] Kaczorek T. (1985): Two Dimensional Linear Systems.— Berlin: Springer.
- [12] Kaczorek T. (1995): Generalized 2D continuous-discrete linear systems with delays.—Appl. Math. Comp. Scince, Vol. 5, No. 3, pp. 439–454.
- [13] Khurgin Ya.I. and Yakovlev V.P. (1971): Finite Functions in Physics and Technics.—Moscow: Nauka, (in Russian).
- [14] Perov K.A. (1975): Optimal Control for Problems of Mathematical Physics.—Moscow: Nauka, (in Russian).
- [15] Rashevski P.K. (1947): Geometric Theory of Partial Differential Equations.—Moscow: Nauka, (in Russian).
- [16] Shankar S. and Willems J. (2000): Behaviours of nD distributed systems. — Proc. 2nd Int. Workshop Multidimensional (nD) Systems, (NDS-2000), Zielona Góra, Poland, pp. 23–30.
- [17] Vasilyev F.P. (1981): Numerical Methods for Extremal Problems.— Moscow: Nauka, (in Russian).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ1-0002-0004