Controllability decomposition of dynamic-algebraic Boolean control networks

ABSTRACTTwo types of controllability of dynamic-algebraic Boolean control networks are first presented. The necessary and sufficient conditions of such controllability are derived. A similar concept of coordinate transformation called special restricted coordinate transformation is posed. It is sufficient to transform the coordinate frame of a dynamic-algebraic Boolean control network and obtain its corresponding equivalent form. The relevant results about special restricted coordinate transformation are proposed. Accordingly, two kinds of controllability decomposition are discussed and the corresponding algorithms are provided, which differs from that of the conventional Boolean networks. A method is provided to guarantee that all the dynamic equations in controllable subsystem are affected by control. A numerical example and a practical example are raised to illustrate the results of this paper, and the latter one is about the programmable logical circuit.