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Stochastic controllability of linear systems with state delays

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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.
Twórcy
autor
  • Institute of Control Engineering, Silesian University of Technology ul. Akademicka 16, 44–100 Gliwice, Poland, jerzy.klamka@polsl.pl
Bibliografia
  • [1] Arapostathis A., George R.K., Ghosh M.K. (2001): On the controllability of a class of nonlinear stochastic systems. - Syst. Contr. Lett., Vol. 44, No. 1, pp. 25-34.
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  • [15] Mahmudov N.I. (2001): Controllability of linear stochastic systems in Hilbert spaces.-J. Math. Anal. Applic., Vol. 259, No. 1, pp. 64-82.
  • [16] 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.
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Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ1-0041-0007
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