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2009 | 19 | 4 | 597-608
Tytuł artykułu

Time-optimal control of infinite order hyperbolic systems with time delays

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, the time-optimal control problem for infinite order hyperbolic systems in which time delays appear in the integral form both in state equations and in boundary conditions is considered. Optimal controls are characterized in terms of an adjoint system and shown to be unique and bang-bang. These results extend to certain cases of nonlinear control problems. The particular properties of optimal control are discussed.
Rocznik
Tom
19
Numer
4
Strony
597-608
Opis fizyczny
Daty
wydano
2009
otrzymano
2008-10-28
Twórcy
  • Institute of Automatics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Cracow, Poland
Bibliografia
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  • Dubinskij, J. A. (1975). Sobolev spaces of infinite order and behavior of solution of some boundary value problems with unbounded increase of the order of the equation, Matiematiczeskii Sbornik 98: 163-184.
  • Dubinskij, J. A. (1976). Non-trivality of Sobolev spaces of infinite order for a full euclidean space and a torus, Matiematiczeskii Sbornik 100: 436-446.
  • Dubinskij, J. A. (1986). Sobolev Spaces of Infinite Order and Differential Equations, Teubner-Texte zur Mathematik, Vol. 87, Teubner-Verlag, Leipzig.
  • Dunford, N. and Schwartz, J. (1958). Linear Operators, Vol. 1, John Wiley and Sons, New York, NY.
  • El-Saify, H. A. and Bahaa, G. M. (2002). Optimal control for n × n hyperbolic systems involving operators of infinite order, Mathematica Slovaca 52: 409-422.
  • Friedman, A. (1969). Partial Differential Equations, Holt, Reinhart and Winston, New York, NY.
  • Knowles, G. (1978). Time optimal control of parabolic systems with boundary conditions involving time delays, Journal of Optimization Theory and Applications 25(4): 563-574.
  • Kowalewski, A. (1993a). Boundary control of hyperbolic system with time lags, IMA Journal of Mathematical Control and Information 10: 261-272.
  • Kowalewski, A. (1993b). Optimal control of hyperbolic system with time lags, Applied Mathematics and Computer Science 3(4): 687-697.
  • Kowalewski, A. (1995). Optimal control of hyperbolic system with time-varying lags, IMA Journal of Mathematical Control and Information 12: 133-143.
  • Kowalewski, A. (1998). Optimal control of a distributed hyperbolic system with multiple time-varying lags, International Journal of Control 71: 419-435.
  • Kowalewski, A. (2000). Optimal control of distributed hyperbolic systems with deviating arguments, International Journal of Control 73: 1026-1041.
  • Kowalewski, A. (2003). Time-optimal control problem of hyperbolic systems with deviating arguments, International Journal of Control 76: 557-565.
  • Lions, J. (1971). Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, Berlin/Heidelberg.
  • Lions, J. and Magenes, E. (1972). Non-Homogeneous Boundary Value Problems and Applications, Vols. 1 and 2, Springer-Verlag, Berlin/Heidelberg.
  • Olech, C. (1966). Extremal solutions of a control system, Journal of Differential Equations 2: 74-101.
  • Tanabe, H. (1965). On differentiability and analyticity of weighted elliptic boundary-value problems, Osaka Mathematical Journal 2: 163-190.
  • Wang, P. K. C. (1975). Optimal control of parabolic systems with boundary conditions involving time delays, SIAM Journal of Control 13(2): 274-293.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv19i4p597bwm
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