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Identifying a linear system model from data has wide applications in controltheory. The existing work on finite sample analysis for linear systemidentification typically uses data from a single system trajectory under i.i.drandom inputs, and assumes that the underlying dynamics is truly linear. Incontrast, we consider the problem of identifying a linearized model when thetrue underlying dynamics is nonlinear. We provide a multiple trajectories-baseddeterministic data acquisition algorithm followed by a regularized leastsquares algorithm, and provide a finite sample error bound on the learnedlinearized dynamics. Our error bound demonstrates a trade-off between the errordue to nonlinearity and the error due to noise, and shows that one can learnthe linearized dynamics with arbitrarily small error given sufficiently manysamples. We validate our results through experiments, where we also show thepotential insufficiency of linear system identification using a singletrajectory with i.i.d random inputs, when nonlinearity does exist.

Learning Linearized Models from Nonlinear Systems with Finite Data