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2007 | 17 | 1 | 5-13
Tytuł artykułu

Stochastic controllability of linear systems with state delays

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A class of finite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with a single point delay in the state variables is considered. Using a theorem and methods adopted directly from deterministic controllability problems, necessary and sufficient conditions for various kinds of stochastic relative controllability are formulated and proved. It will be demonstrated that under suitable assumptions the relative controllability of an associated deterministic linear dynamic system is equivalent to the stochastic relative exact controllability and the stochastic relative approximate controllability of the original linear stochastic dynamic system. Some remarks and comments on the existing results for the controllability of linear dynamic systems with delays are also presented. Finally, a minimum energy control problem for a stochastic dynamic system is formulated and solved.
Rocznik
Tom
17
Numer
1
Strony
5-13
Opis fizyczny
Daty
wydano
2007
otrzymano
2006-11-15
poprawiono
2007-01-08
Twórcy
autor
  • Institute of Control Engineering, Silesian University of Technology, ul. Akademicka 16, 44-100 Gliwice, Poland
Bibliografia
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  • Bashirov A.E. and Mahmudov N.I. (1999): On concepts of controllability for deterministic and stochastic systems. - SIAM J. Contr. Optim., Vol.37, No.6, pp.1808-1821.
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  • Fernandez-Cara E., Garrido-Atienza M.J. and Real J. (1999): On the approximate controllability of a stochastic parabolic equation with multiplicative noise. - C.R. Acad. Sci. Paris, t.328, Sèrie1, pp.675-680.
  • Kim Jong Uhn (2004): Approximate controllability of a stochastic wave equation. - Appl. Math.Optim., Vol.49, No.1, pp.81-98.
  • Klamka J. (1991): Controllability of Dynamical Systems. - Dordrecht: Kluwer Academic.
  • Klamka J. (1993): Controllability of dynamical systems-A survey. - Arch. Contr. Sci., Vol.2, No.3/4, pp.281-307.
  • Klamka J. (1996): Constrained controllability of nonlinear systems. - J. Math. Anal. Applic., Vol.201, No.2, pp.365-374.
  • Klamka J. (2000): Schauder's fixed point theorem in nonlinear controllability problems. - Contr.Cybern., Vol.29, No.3, pp.377-393.
  • Klamka J. and Socha L. (1977): Some remarks about stochastic controllability. - IEEE Trans.Automat. Contr., Vol.AC-22, No.5, pp.880-881.
  • Klamka J. and Socha L. (1980): Some remarks about stochastic controllability for delayed linear systems. - Int. J. Contr., Vol.32, No.3, pp.561-566.
  • Mahmudov N.I. (2001): Controllability of linear stochastic systems. - IEEE Trans. Automat. Contr., Vol.AC-46, No.4, pp.724-731.
  • Mahmudov N.I. (2001): Controllability of linear stochastic systems in Hilbert spaces. - J. Math.Anal. Applic., Vol.259, No.1, pp.64-82.
  • Mahmudov N.I. (2002): On controllability of semilinear stochastic systems in Hilbert spaces. - IMA J. Mathemat. Contr. Inf., Vol.19, No.2, pp.363-376.
  • Mahmudov N.I. (2003): Controllability and observability of linear stochastic systems in Hilbert spaces. - Progress in Probability, Vol.53, No.1, pp.151-167.
  • Mahmudov N.I. (2003): Approximate controllability of semilinear deterministic and stochastic evolution equations in abstract spaces. - SIAM J. Contr.Optim., Vol.42, No.5, pp.1604-1622.
  • Mahmudov N.I. and Denker A. (2000): On controllability of linear stochastic systems. - Int. J.Contr., Vol.73, No.2, pp.144-151.
  • Mahmudov N.I. and Zorlu S. (2003): Controllability of nonlinear stochastic systems. - Int. J.Contr., Vol.76, No.2, pp.95-104.
  • Subramaniam R. and Balachandran K. (2002): Controllability of stochastic Volterra integrodifferential systems. - Korean J. Comput. Appl. Math., Vol.9, No.2, pp.583-589.
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  • Zabczyk J. (1991): Controllability of stochastic linear systems. - Syst. Contr. Lett., Vol.1, No.1, pp.25-31
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Bibliografia
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