On system identification of complex systems from finite data

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We introduce a new principle for identification based on choosing a model from the model-parameterization, which best approximates the unknown real system belonging to a more complex space of systems that do not lend themselves to a finite-parameterization. The principle is particularly effective for robust control as it leads to a precise notion of parametric and nonparametric error, and the identification problem can be equivalently perceived as that of robust convergence of the parameters in the face of unmodeled errors. The main difficulty in its application stems from the interplay of noise and unmodeled dynamics and requires developing novel two-step algorithms that amount to annihilation of the unmodeled error followed by averaging out the noise. The paper establishes: robust convergence for a large class of systems, topologies, and unmodeled errors; sample path based finite-time polynomial rate of convergence; and annihilation-correlation algorithms for linearly parameterized model structures.