Identification of Multivariable Hammerstein Systems with Hysteresis Nonlinearities

This paper addresses the problem of identification of multivariable systems exhibiting hysteresis through the application of the Hammerstein model. The Hammerstein model consists of a generalized rate-dependent Prandtl-Ishlinskii hysteresis block followed by a linear dynamic representation in state space, with both components being multivariable. Building on this framework, we develop a novel identification methodology that integrates a modified version of a particle swarm optimization algorithm, extended to handle multivariable scenarios, along with a subspace algorithm based on harmonic signals. The proposed methodology is tested on two numerical examples. The results suggest that our method is capable to identify models that effectively capture asymmetric hysteresis in coupled, non-minimal phase multivariable systems, even under conditions of white measurement noise.