Data-driven Identification of Approximate Passive Linear Models for Nonlinear Systems

In model-based learning, it is desirable for the learned model to preserve structural properties of the system that may facilitate easier control design or provide performance, stability or safety guarantees. Here, we consider an unknown nonlinear system possessing such a structural property passivity, that can be used to ensure robust stability with a learned controller. We present an algorithm to learn a passive linear model of this nonlinear system from time domain input-output data. We first learn an approximate linear model of this system using any standard system identification technique. We then enforce passivity by perturbing the system matrices of the linear model, while ensuring that the perturbed model closely approximates the input-output behavior of the nonlinear system. Finally, we derive a trade-off between the perturbation size and the radius of the region in which the passivity of the linear model guarantees local passivity of the unknown nonlinear system.