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This paper considers the problem of learning models to be used for controller design. Using a simple example, it argues that in this scenario the objective should reflect the closed-loop, rather than open-loop distance between the learned model and the actual plant, a task that can be accomplished by using a gap metric motivated approach. This is particularly important when identifying open-loop unstable plants, since typically in this case the open-loop distance is unbounded. In this context, the paper proposes a convex optimization approach to learn its coprime factors. This approach has a dual advantage: (1) it can easily handle open-loop unstable plants, since the coprime factors are stable, and (2) it is "self certified", since a simple norm computation on the learned factors indicates whether or not a controller designed based on these factors will stabilize the actual (unknown) plant. If this test fails, it indicates that further learning is needed.more » « less
