SOLSP a New Algorithm to Reduce The Complexity Time of Controllability Matrix

Controllability represents a simplified description of the ability of a system to fully control a system or subsystem. Besides, the way of transferring the system from the primary state to the desired state. Techniques of controlling various networks become very important for use to control networks in health care, medical, engineering, train, water and electricity lines, airport, the human brain, traffic lights, municipalities, technical and social networks for the purpose of facilitating the necessary controllability over the hills nodes with minimal effort, cost and maximized speed. The controllability approach starts with converting graph to a matrix, compute controllability matrix with the traditional method, convert controllability matrix to Row Echelon Form (REF). Then compute rank for each matrix, and calculate the Quantitative Controllability Index (Q) of the network quantitatively. The time complexity of this approach is very high. Therefore, a developed or a new algorithm named Search Output Link Save Position (SOLSP) is significant to be proposed to enhance or minimize the required time to compute the network controllability. SOLSP gave exactly the same results in a very short time.