An efficient atomic norm minimization approach to identification of low order models

Many practical situations involve synthesizing controllers for systems where a priori models are not available and thus must be identified from experimental data. In these cases it is of interest to identify the simplest model compatible with the available information, since the order of the model is usually reflected in the order of the resulting controllers. The main result of this paper is a computationally efficient algorithm to identify low order models from mixed time/frequency domain data. We propose two algorithms: one deterministic, based on semi-algebraic optimization, and the second based on a randomized approach. As shown here, both algorithms are guaranteed to converge to the optimum. A salient feature of the proposed approach is its ability to accommodate mixed time/frequency domain data without the need to resort to finite truncations or enforcing interpolation type constraints.