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2015 | 25 | 2 | 207-215
Tytuł artykułu

Controllability of nonlinear stochastic systems with multiple time-varying delays in control

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper is concerned with the problem of controllability of semi-linear stochastic systems with time varying multiple delays in control in finite dimensional spaces. Sufficient conditions are established for the relative controllability of semilinear stochastic systems by using the Banach fixed point theorem. A numerical example is given to illustrate the application of the theoretical results. Some important comments are also presented on existing results for the stochastic controllability of fractional dynamical systems.
Rocznik
Tom
25
Numer
2
Strony
207-215
Opis fizyczny
Daty
wydano
2015
otrzymano
2014-01-17
poprawiono
2014-08-05
Twórcy
  • Department of Mathematics, Periyar University, Salem 636 011, India
  • Department of Mathematics, Bharathiar University, Coimbatore 641 046, India
  • Department of Mathematics, Periyar University, Salem 636 011, India
Bibliografia
  • Balachandran, K., and Karthikeyan, S. (2009). Controllability of stochastic systems with distributed delays in control, International Journal of Control 82(7): 1288-1296.
  • Balachandran, K., Kokila, J. and Trujillo, J.J. (2012). Relative controllability of fractional dynamical systems with multiple delays in control, Computers & Mathematics with Applications 64(10): 3037-3045.
  • Basin, M., Rodriguez-Gonzaleza, J. and Martinez-Zunigab, M. (2004). Optimal control for linear systems with time delay in control input, Journal of the Franklin Institute 341(1): 267-278.
  • Dauer, J.P., Balachandran, K. and Anthoni, S.M. (1998). Null controllability of nonlinear infinite neutral systems with delays in control, Computers & Mathematics with Applications 36(1): 39-50.
  • Enrhardt, M. and W. Kliemann, W. (1982). Controllability of stochastic linear systems, Systems and Control Letters 2(3): 145-153.
  • Gu, K. and Niculescu, S.I. (2003). Survey on recent results in the stability and control of time-delay systems, ASME Transactions: Journal of Dynamic Systems, Measurement, and Control 125(2): 158-165.
  • Guendouzi, T. and Hamada, I. (2013). Relative controllability of fractional stochastic dynamical systems with multiple delays in control, Malaya Journal of Matematik 1(1): 86-97.
  • Guendouzi, T. and Hamada, I. (2014). Global relative controllability of fractional stochastic dynamical systems with distributed delays in control, Sociedade Paranaense de Matematica Boletin 32(2): 55-71.
  • Karthikeyan, S. and Balachandran, K. (2013). On controllability for a class of stochastic impulsive systems with delays in control, International Journal of Systems Science 44(1): 67-76.
  • Klamka, J. (1976). Controllability of linear systems with time-variable delays in control, International Journal of Control 24(2): 869-878.
  • Klamka, J. (1978). Relative controllability of nonlinear systems with distributed delays in control, International Journal of Control 28(2): 307-312.
  • Klamka, J. (1980). Controllability of nonlinear systems with distributed delay in control, International Journal of Control 31(1): 811-819.
  • Klamka, J. (1991). Controllability of Dynamical Systems, Kluwer Academic Publishers, Dordrecht.
  • Klamka, J. (2000). Schauder’s fixed point theorem in nonlinear controllability problems, Control and Cybernetics 29(2): 153-165.
  • Klamka, J. (2007a). Stochastic controllability of linear systems with delay in control, Bulletin of the Polish Academy of Sciences: Technical Sciences 55(1): 23-29.
  • Klamka, J. (2007b). Stochastic controllability of linear systems with state delays, International Journal of Applied Mathematics and Computer Science 17(1): 5-13, DOI: 10.2478/v10006-007-0001-8.
  • Klamka, J. (2008a). Stochastic controllability of systems with variable delay in control, Bulletin of the Polish Academy of Sciences: Technical Sciences 56(3): 279-284.
  • Klamka, J. (2008b). Stochastic controllability and minimum energy control of systems with multiple delays in control, Applied Mathematics and Computation 206(2): 704-715.
  • Klamka, J. (2009). Constrained controllability of semilinear systems with delays, Nonlinear Dynamics 56(4): 169-177.
  • Klamka, J. (2013), Controllability of dynamical systems. A survey, Bulletin of the Polish Academy of Sciences: Technical Sciences 61(2): 335-342.
  • Klein, E.J. and Ramirez, W.F. (2001). State controllability and optimal regulator control of time-delayed systems, International Journal of Control 74(3): 281-89.
  • Li, W. (1970). Mathematical Models in the Biological Sciences, Master’s thesis, Brown University, Providence, RI.
  • Mahmudov, N.I. (2001). Controllability of linear stochastic systems, IEEE Transactions on Automatic Control 46(1): 724-731.
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  • Mahmudov, N.I., and Zorlu, S. (2003). Controllability of nonlinear stochastic systems, International Journal of Control 76(2): 95-104.
  • Oksendal, B. (2003). Stochastic Differential Equations. An Introduction with Applications, Sixth Edition, Springer-Verlag, Berlin.
  • Richard, J.P. (2003). Time-delay systems: An overview of some recent advances and open problems, Automatica 39(10): 1667-1694.
  • Somasundaram, D. and Balachandran, K. (1984). Controllability of nonlinear systems consisting of a bilinear mode with distributed delays in control, IEEE Transactions on Automatic Control AC-29(2): 573-575.
  • Shen, L., and Sun, J. (2012). Relative controllability of stochastic nonlinear systems with delay in control, Nonlinear Analysis: Real World Applications 13(1): 2880-2887.
  • Sikora, B. and Klamka, J. (2012). On constrained stochastic controllability of dynamical systems with multiple delays in control, Bulletin of the Polish Academy of Sciences: Technical Sciences 60(2): 301-305.
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Typ dokumentu
Bibliografia
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