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This paper concerns identification of uncontrolled or closed loop nonlinearsystems using a set of trajectories that are generated by the system in adomain of attraction. The objective is to ensure that the trajectories of theidentified systems are close to the trajectories of the real system, asquantified by an error bound that is prescribed a priori. A majority ofexisting methods for nonlinear system identification rely on techniques such asneural networks, autoregressive moving averages, and spectral decompositionthat do not provide systematic approaches to meet pre-defined error bounds. Thedeveloped method is based on Carleman linearization-based lifting of thenonlinear system to an infinite dimensional linear system. The linear system isthen truncated to a suitable order, computed based on the prescribed errorbound, and parameters of the truncated linear system are estimated from data.The effectiveness of the technique is demonstrated by identifying anapproximation of the Van der Pol oscillator from data within a prescribed errorbound.

Carleman Lifting for Nonlinear System Identification with Guaranteed Error Bounds