Abstract:

Determining which dynamical systems exhibit behavior most similar to a target system is critical for transfer learning and data-efficient system identification. However, quantifying similarity between nonlinear systems from input-output data is challenging: trajectories differ in length, initial conditions, and input sequences, making direct comparison unreliable. Classical system identification depends on correct model structure selection, while frequencydomain methods often miss transient dynamics. This paper proposes a data-driven methodology based on matrix profiles: a time-series tool for efficient subsequence matching. The approach operates directly on input-output trajectories without state estimation or parameter identification. By embedding trajectories in an interleaved inputoutput space and computing cross-matrix profiles, the method captures dynamical features including transient behavior under varying conditions. We derive analytical bounds on matrix profile distance as functions of parameter and input discrepancies, establishing that systems closer in parameter space yield smaller matrix profile distances when control trajectories are similar. Numerical experiments demonstrate improved similarity assessment compared to Euclidean distance and dynamic time warping baselines, achieving substantial reductions in trajectory error and parameter-space deviation across both linear and nonlinear systems.