Efficient and systematic identification of MIMO bilinear state space models

We present a systematic way to identify multi-input, multioutput (MIMO) bilinear state space systems subject to white noise inputs, in the presence of process and measurement noise. The algorithm we present is based on a family of subspace identification algorithms for linear systems. It requires the linear pair (A, C) to be observable. We use subspace identification to determine the model order, to identify the linear part of the model, and to compute an initial estimate for the nonlinear part. The final estimate of the nonlinear part is computed by numerically solving a nonlinear optimization problem. A series of simulation experiments showed that the initial estimate is close to the optimum and allows convergence of the nonlinear optimization problem.