Identification of State-space Linear Time-varying Systems with Sum-of-norms Regularization

In this paper, we propose a method for the estimation of state-space models for linear time-varying systems using sum-of-norms regularization. Specifically, the system parameters are assumed to follow a probability distribution with a Markovian dependency across time samples. This prior information is incorporated in a Bayesian framework, which leads to a maximum-a-posteriori criterion involving a sum-of-norms penalty term. The resulting estimation problem is addressed with a generalized expectation maximization algorithm, whose maximization step consists of a 'difference of convex' optimization problem, for which a monotone procedure is established. Controlled computational experiments using synthetic data are performed to show the effectiveness of the approach. The proposed algorithm is expected to find practical application in modeling dynamical processes arising in different domains, particularly in the fields of economics and neuroscience.