A new approach for global controllability of higher order Boolean control network

Using the semi-tensor product, the global control problem of higher order Boolean control network is considered. Firstly, the number of different control sequences that drive the higher order Boolean control network from the initial state to the destination state while avoiding undesirable set is provided. Then, the definition of global controllability of higher order Boolean control network is given. Thirdly, by using the classical theory of nonnegative matrices, the necessary and sufficient condition for the global controllability of higher order Boolean control network is presented. At last, an example is given to illustrate the main results.