Controllability analysis of directed networks based on pruning motif isomorph

Abstract

The current driver nodes search methods are difficult to cope with large networks, and the solution process does not consider the cost of control imposed by the nodes. In order to solve the problem of control input to achieve control synchronization in finite states for networks with different node costs, this paper proposes a pruning and motif isomorph search method for a driver node set. Firstly, we prove the sufficient conditions for the network to be strictly controllable under partial nodes control, then we classify the nodes and prove the equivalence controllability of the pruning network, and then we establish three models of maximum augmenting path search, local pruning and motif matching to form a complete driver node set search algorithm. Finally, the algorithm is validated by three types of experiments: examples, classical networks and real networks. The results show that our method not only guarantees the accuracy of the search results, but also has lower time complexity than other existing methods, which can efficiently handle large networks, and no more than 16.84% of the maximum driver nodes can control the whole network.