Data-Driven Simulation of Generalized Bilinear Systems via Linear Time-Invariant Embedding

Nonparameteric representations of linear time-invariant systems that use Hankel matrices constructed from data are the basis for data-driven simulation and control. This article extends the approach to data-driven simulation of a class of nonlinear systems, called generalized bilinear. The generalized bilinear class includes Hammerstein, finite-lag Volterra, and bilinear systems. The key step of the generalization is an embedding result that is of independent interest. The behavior of a nonlinear system is included into the behavior of a linear time-invariant system. The method proposed is illustrated and compared with a model-based method on simulation examples and real-life data.