College of Science

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.

Stochastic differential equations are one of the most useful areas of the theory of stochastic processes and its applications in mathematics.Some nonlinear (Itô) dynamic stochastic control system driven by
Brownian motion 2 based on dynamic observer have been considered.Output feedback (observer – based) robust and optimal control law which guarantees global (local) asymptotic stable in probability for the

The main objectives of this thesis, is oriented toward function approximation using special type of spline functions, which is called the “Gspline “including the details of the subject. The second objective consider the 1st  order ordinary differential equations of the form: .
y'(x)=F(x,y),   x ∈[a,b]