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

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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.
Twórcy
  • Department of Mathematics, Periyar University, Salem 636 011, India
  • Department of Mathematics, Bharathiar University, Coimbatore 641 046, India
autor
  • Department of Mathematics, Periyar University, Salem 636 011, India
Bibliografia
  • [1] Balachandran, K. (1987). Global relative controllability of nonlinear systems with time-varying multiple delays in control, International Journal of Control 46(1): 193–200.
  • [2] Balachandran, K. and Dauer, J.P. (1996). Null controllability of nonlinear infinite delay systems with time varying multiple delays in control, Applied Mathematics Letters 9(3): 115–121.
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  • [4] 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.
  • [5] 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.
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  • [9] 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.
  • [10] 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.
  • [11] 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.
  • [12] Klamka, J. (1976). Controllability of linear systems with time-variable delays in control, International Journal of Control 24(2): 869–878.
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  • [16] Klamka, J. (2000). Schauder’s fixed point theorem in nonlinear controllability problems, Control and Cybernetics 29(2): 153–165.
  • [17] 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.
  • [18] 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.
  • [19] 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.
  • [20] Klamka, J. (2008b). Stochastic controllability and minimum energy control of systems with multiple delays in control, Applied Mathematics and Computation 206(2): 704–715.
  • [21] Klamka, J. (2009). Constrained controllability of semilinear systems with delays, Nonlinear Dynamics 56(4): 169–177.
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Bibliografia
Identyfikator YADDA
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