Stochastic Controllability of Linear Systems With State Delays

Stochastic Controllability of Linear Systems With State Delays 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.

[1]  K. Balachandran,et al.  Controllability of stochastic Volterra integrodifferential systems , 2002 .

[2]  Nazim I. Mahmudov,et al.  On controllability of semilinear stochastic systems in Hilbert spaces , 2002 .

[3]  Nazim I. Mahmudov,et al.  Controllability and Observability of Linear Stochastic Systems in Hilbert Spaces , 2003 .

[4]  Jerzy Klamka,et al.  Some remarks about stochastic controllability for delayed linear systems , 1980 .

[5]  Han-Fu Chen,et al.  On the Stochastic Observability and Controllability , 1978 .

[6]  Mrinal K. Ghosh,et al.  On the controllability of a class of nonlinear stochastic systems , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[7]  W. Kliemann,et al.  Controllability of linear stochastic systems , 1982 .

[8]  Jerzy Klamka.  Constrained controllability of nonlinear systems , 1995 .

[9]  Nazim I. Mahmudov,et al.  On controllability of linear stochastic systems , 2000 .

[10]  Nazim I. Mahmudov,et al.  Controllability of semilinear stochastic systems in Hilbert spaces , 2003 .

[11]  Nazim I. Mahmudov,et al.  Controllability of Linear Stochastic Systems in Hilbert Spaces , 2001 .

[12]  J. Klamka.  Controllability of dynamical systems , 1991, Mathematica Applicanda.

[13]  Nazim I. Mahmudov,et al.  Approximate Controllability of Semilinear Deterministic and Stochastic Evolution Equations in Abstract Spaces , 2003, SIAM J. Control. Optim..

[14]  Jong Uhn Kim.  Approximate Controllability of a Stochastic Wave Equation , 2004 .

[15]  Nazim I. Mahmudov,et al.  On Concepts of Controllability for Deterministic and Stochastic Systems , 1999 .

[16]  Yoshifumi Sunahara,et al.  On stochastic controllability for nonlinear systems , 1974 .

[17]  Pagavathigounder Balasubramaniam,et al.  Controllability of semilinear stochastic evolution equations in Hilbert space. , 2001 .

[18]  Jerzy Klamka.  Schauder's fixed-point theorem in nonlinear controllability problems , 2000 .

[19]  Jerzy Klamka,et al.  Some remarks about stochastic controllability , 1977 .

[20]  Nazim I. Mahmudov,et al.  Controllability of non-linear stochastic systems , 2003 .

[21]  Enrique Fernández-Cara,et al.  On the approximate controllability of a stochastic parabolic equation with a multiplicative noise , 1999 .

[22]  Agamirza E. Bashirov,et al.  On Controllability Conception for Stochastic Systems , 1997 .

[23]  Jerzy Zabczyk,et al.  Controllability of stochastic linear systems , 1981 .

[24]  Ari Arapostathis,et al.  On the controllability of a class of nonlinear stochastic systems , 2001, Syst. Control. Lett..