Subspace Identification of Local 1D Homogeneous Systems

This paper studies the local subspace identification of 1D homogeneous networked systems. The main challenge lies at the unmeasurable interconnection signals between neighboring subsystems. Since there are many unknown inputs to the concerned local system, the corresponding identification problem is semi-blind. To cope with this problem, a nuclear norm optimization based subspace identification is presented, which is carried out for solving the Markov parameters of a locally lifted system, followed by determining the system matrices of a single subsystem. In the step of Markov parameter estimation, we form a nuclear norm regularized optimization problem which can well handle the adverse effects of the unknown system inputs as long as the number of unknown system inputs is relatively small. In the step of system realization, we again derive a nuclear norm regularized optimization formulation which can cope with the under-determinedness of the realization problem. In the end, the overall identification algorithm is summarized.