Nuclear norm system identification with missing inputs and outputs

We present a system identification method for problems with partially missing inputs and outputs. The method is based on a subspace formulation and uses the nuclear norm heuristic for structured low-rank matrix approximation, with the missing input and output values as the optimization variables. We also present a fast implementation of the alternating direction method of multipliers (ADMM) to solve regularized or non-regularized nuclear norm optimization problems with Hankel structure. This makes it possible to solve quite large system identification problems. Experimental results show that the nuclear norm optimization approach to subspace identification is comparable to the standard subspace methods when no inputs and outputs are missing, and that the performance degrades gracefully as the percentage of missing inputs and outputs increases.