UIUC researchers generalize behavioral approach for nonlinear system modeling

Researchers Boya Hou and Maxim Raginsky at the University of Illinois Urbana-Champaign have published a paper generalizing Jan Willems' behavioral approach to discrete-time nonlinear systems within a vector-valued reproducing kernel Hilbert space (RKHS). This framework extends beyond linear time-invariant systems to cover nonlinear models such as Volterra series, their autoregressive variants, and Hammerstein-type state-space realizations. The work addresses the challenge of data-driven modeling when simulation or control objectives must be achieved without an explicit system identification step, a common need in modern cyber-physical and autonomous systems.

The paper links the behavioral framework to two specific data-driven modeling methods in RKHS: minimum-norm interpolation and subspace identification. By treating the system's behavior directly from data rather than through a parametric model, the approach reduces reliance on prior knowledge of system dynamics. This is particularly relevant for nonlinear systems where identification is difficult. The work is published in arXiv with 12 pages and opens new pathways for controlling complex systems using only measurement data, with potential applications in robotics, power grids, and biomedical engineering.