*1.3. Controllability*

In mathematical control theory, controllability and optimal control are two important concepts. In controllability, one studies the steering of a dynamical system from a given initial state to any other state or in the neighborhood of the state under some admissible control input. The cases where target states are defined in a given subregion are particularly very important; this situation arises in many real world applications. The last few decades have seen tremendous work in the controllability problems for integer order systems. Several techniques have been developed for solving such problems [7,8]. It has been seen that mostly authors worked on the problems with hard constraints on the state or control. This is mainly due to its applicability and importance in various applications in optimal control. Moreover, many authors have studied controllability of the semilinear, partial evolution equations, we refer to [9–17] and references therein. In a very interesting paper [14], Kenichi Fujishiro and Masahiro Yamamoto consider a partial differential equations with fractional order time derivatives and established approximate controllability by interior control.
