Identification of Sparse Continuous-Time Linear Systems with Low Sampling Rate: Optimization Approaches

Abstract: This paper addresses identification of sparse linear and noise-driven continuous-time state-space systems, i.e., the right-hand sides in the dynamical equations depend only on a subset of the states. The key assumption in this study, is that the sample rate is not high enough to directly infer the continuous time system from the data. This assumption is relevant in applications where sampling is expensive or requires human intervention (e.g., biomedicine applications). We propose an iterative optimization scheme with $l_1$-regularization, where the search directions are restricted those that decrease prediction error in each iteration. We provide numerical examples illustrating the proposed method; the method outperforms the least squares estimation for large noise.