Identification of network topology via quadratic optimization

Identification of network topology is to estimate the topology of a controllable and observable network with given number of nodes such that the identified network will satisfy the response between specified input and observed output. This paper examines the network topology identification (NTI) problems to find the original graph Laplacian from input-output data. A `similar´ set of state-space matrices satisfying the input-output response is firstly constructed through system identification procedure. Based on the similarity relationship, we reformulate the NTI problems as general Quadratically Constrained Quadratic Programming (QCQP) problems. The QCQP problem is then transformed into semidefinite programming (SDP) problem with a rank one constraint. An iterative rank minimization method is proposed to gradually approach the optimal solution. Examples are presented to verify the convergence of the proposed method.