System Identification: A Learning Theory Approach
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In this paper, the problem of system identification is formulated as a problem in statistical learning theory. It is shown that if a particular type of uniform convergence result holds, then the traditional approach of choosing the current model to minimize the error on the observed data will eventually converge to an optimal model within the specified class. More important, the reformulation of system identification as a learning theory problem leads tofinite time estimatesfor the rate at which the estimated model converges to the optimal model. As an illustration of the approach, a result is derived showing that in the case of exponentially stable systems with fading memory, the desired uniform convergence result holds, so that the learning theory approach is applicable,providede the adjustable parameters enter the system model in a linear fashion.
KeywordsSystem identification Statistical learning Pseudo-dimension Uniform convergence Empirical means
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