  Gray-box identification is prevalent in modeling physical and networked
systems. However, due to the non-convex nature of the gray-box identification
problem, good initial parameter estimates are crucial for a successful
application. In this paper, a new identification method is proposed by
exploiting the low-rank and structured Hankel matrix of impulse response. This
identification problem is recasted into a difference-of-convex programming
problem, which is then solved by the sequential convex programming approach
with the associated initialization obtained by nuclear-norm optimization. The
presented method aims to achieve the maximum impulse-response fitting while not
requiring additional (non-convex) conditions to secure non-singularity of the
similarity transformation relating the given state-space matrices to the
gray-box parameterized ones. This overcomes a persistent shortcoming in a
number of recent contributions on this topic, and the new method can be applied
for the structured state-space realization even if the involved system
parameters are unidentifiable. The method can be used both for directly
estimating the gray-box parameters and for providing initial parameter
estimates for further iterative search in a conventional gray-box
identification setup.
