On Controllability Probabilities of Stochastic non – linear Control Systems

The main aim of this thesis is focused on studying some non-linear uncertain stochastic dynamical system.The necessary background for stochastic process, stochastic integral for Brownian motion and fractional Brownian motion, stochastic dynamical system driven by Brownian motion and fractional Brownian motion are studied and discussed supported by useful comments and examples. Ito Some class of non-linear   stochastic ordinary control system driven by Brownian motion as well as fractional Brownian motion have been considered and discussed. A necessary theorem of solvability and controllability of some class of non-linear  dynamical control system driven by Brownian motion are Ito discussed and prove d using Banach fixed point theorem and supported by useful concluding remark and illustration.ˆ
Ito A theorem of solvability and controllability of som e class of non-linear  dynamical system driven by fractional Brownian motion are also stated and prove d supported by illustration.