Improved rates for identification of partially observed linear dynamical systems
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Identification of a linear time-invariant dynamical system from partial observations is a fundamental problem in control theory. A natural question is how to do so with non-asymptotic statistical rates depending on the inherent dimensionality (order) d of the system, rather than on the sufficient rollout length or on 1/1-ρ(A), where ρ(A) is the spectral radius of the dynamics matrix. We develop the first algorithm that given a single trajectory of length T with gaussian observation noise, achieves a near-optimal rate of O(√(%s/%s)dT) in ℋ_2 error for the learned system. We also give bounds under process noise and improved bounds for learning a realization of the system. Our algorithm is based on low-rank approximation of Hankel matrices of geometrically increasing sizes.
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