S-CONTROLLABILITY OF AN ABSTRACT FIRST ORDER SEMILINEAR CONTROL SYSTEM

The objective of this article is to investigate some sufficient conditions, for S-controllability of an abstract first order semilinear control system of the form dx(u)(t) = [Ax(u)(t) + Bu(t) + f(t, x(u)(t))]dt + d omega(t), 0 < t <= T, x(u)(0) = x(0) d xi(u)(t) = Cx(u)(t)dt + dv(t), 0 < t <= T, xi(u)(0) = 0 Here, A is the closed linear operator, B and C are bounded linear operators defined on suitable Hilbert spaces, omega and v are suitable wiener processes, and d is the stochastic differentiation. The results are obtained by the separation principle approach. An example is provided to illustrate the technique.