Data-Driven Sparse System Identification

With their ever-growing size and complexity, real-world dynamical systems are hard to model. Today's systems are complex and large, often with a massive number of unknown parameters which render them doomed to the so-called curse of dimensionality. Therefore, system operators should rely on simple and tractable estimation methods to identify the dynamics of the system via a limited number of recorded input-output interactions, and then design control policies to ensure the desired behavior of the entire system. The area of system identification is created to address this problem [1]. Despite the long history in control theory, most of the results on system identification deal with asymptotic behavior of the proposed estimation methods [1]-[4]. Although these results shed light on the theoretical consistency of these methodologies, they are not applicable to the finite time/sample settings. In many applications, the dynamics of the system should be estimated under the large dimension-small sample size regime, where the dimension of the states and inputs of the system is overwhelmingly large compared to the number of available input-output data. Under such circumstances, the classical approaches for checking the asymptotic consistency of estimators face major breakdowns. Simple examples of such failures can be easily found in high-dimensional statistics.