Data-driven Simulation Using the Nuclear Norm Heuristic

Applications of signal processing and control are classically model-based, involving a two-step procedure for modeling and design: first a model is built from given data, and second, the estimated model is used for filtering, estimation, or control. Both steps typically involve optimization problems, but the combination of both is not necessarily optimal, and the modeling step often ignores the ultimate design objective. Recently, data-driven alternatives are receiving attention, which employ a direct approach combining the modeling and design into a single step. In earlier work, it was shown that data-driven signal processing problems can often be rephrased as missing data completion problems, where the signal of interest is part of an incomplete low-rank mosaic Hankel structured matrix. In this paper, we consider the exact data case and the problem of simulating from a given input, an output trajectory of the unknown data generating system. Our findings suggest that, when using an adequate rescaling of the given data, the exact data-driven simulation problem can be solved by replacing the original structured low-rank matrix completion problem by a convex optimization problem, using the nuclear norm heuristic.