Optimal Driver Set Selection Based On Robustness Of Controllability

In recent years,robustness of structural controllability has been studied by many researchers,considering the changes in the controllability of the system under the failure of nodes or edges.Some studies are based on network connectivity,and characterize robustness through the maximum tolerance to attacks,while others define the robustness based on the increase in the augmented paths caused by node or edge failures.However,there is currently no direct use of the controllable subspace of the damaged network as a robustness indicator.Therefore,this study proposes robustness measures for various node failure strategies,and based on these measures gives a selection of driver node sets to ensure that the system structure is more robust to attacks.Robustness depends on several factors,including strategy,and scale of attacks.Therefore,this paper proposes five robustness indexes based on controllable subspace for different structural attack models.K-RCS is suitable for random node-removal attacks,and G-RCS is suitable for general scenarios including attacks such as node-removals,edge-removals or both.FT-RCS is suitable for highly focused targeted attacks,PT-RCS is suitable for average targeted attacks of smaller scale,GT-RCS is suitable for average targeted attacks of various scale.When robustness of control power of a single driver node is considered,the above-mentioned robustness measures can be used as the centrality indexes of the nodes,which are called K-RCC,G-RCC,FT-RCC,PT-RCC and GT-RCC respectively.Furthermore,based on these robustness measures,a set of driver nodes is selected to make the system more robust against random and targeted attacks.The driver node refers to a node with external input,also known as controlled node.Considering the calculation cost,three effective algorithms are proposed.Method-1 selects the high RCC nodes as the driver nodes.Method-2 selects driver nodes one by one while maximizing the current robustness of driver set for each additional driver node.Method-3 combines RCC and reachability to maximize current robustness of each driver node.These methods provide a trade-off between computational complexity and maximization of robustness.Simulation results show that nodes selected by using RCS and RCC have better controllability when network structure gets damaged.