Towards the minimum-cost control of target nodes in directed networks with linear dynamics

摘要: Abstract Determining an input matrix, i.e., locating predefined number of nodes (named “key nodes”) connected to external control sources that provide signals, so as minimize the cost controlling a preselected subset “target in directed networks is outstanding issue. This problem arises especially large natural and technological networks. To address this issue, we focus on with linear dynamics propose iterative method, termed “L0-norm constraint based projected gradient method” (LPGM) which matrix B involved variable. By introducing chain rule for differentiation, function respect can be derived. allows us search by applying probabilistic projection operator between two spaces, real valued space RN × M L0 norm R L 0 N × M restricting fixed value M. Then, correspond nonzero elements obtained (denoted ) are selected key nodes, each source single node. Simulation examples real-life presented verify potential proposed method. An interesting phenomenon uncovered generally scale free (SF) higher than Erdos-Renyi (ER) using same size target network mean degree. work will deepen understanding optimal problems new insights locate achieving minimum-cost