Partial Approximate Controllability of Semilinear Control Systems

Most of the controllability concepts are for first ordered differential equations, while not all the control systems are of this kind; but by increasing the dimension of the state space, one can rewrite the control system in the form of first ordered differential equations. Therefore, it seems useful to define partial controllability concepts which maintain the original state space. In this thesis, a sufficient condition for partial approximate controllability of semilinear deterministic control systems is proved with a technique which is completely different from the methods using fixed point theorems. More specifically, the partial S-controllability has been weakened for partially observable semilinear stochastic systems and a sufficient condition is provided. The results obtained are demonstrated within examples. Keywords: Controllability, approximate controllability, exact controllability, partial controllability, semilinear systems, stochastic systems.