Guaranteed Structural Controllability For Networked Systems With Minimum Input/Edge Addition

For a networked system with structural controllability, components will be added in the process of operation because of function increase or size increase, which may result in structural uncontrollability of the networked system under original control inputs. With network topology and original control inputs preserved, designing more control inputs or coupling relations to guarantee structural controllability is an important problem. We propose two strategies of adding minimum extra inputs or edges to render a structurally controllable system: 1) through adjusting network topology, minimum input addition problem is transformed into a minimum input selection problem of a simplified network topology, and then a set of minimum additional control inputs is chosen to ensure structural controllability; 2) combining maximum matching sets with greedy algorithm, minimum number of directed edges are added to the system topology to obtain structural controllability. The proposed strategies are able to find an optimal solution of minimum input/edge addition in polynomial time with a low time complexity. We illustrate the validity of our strategies via several graph examples.