Nonparametric System Identification Of Stochastic Switched Linear Systems

We address the problem of learning the parameters of a mean square stable switched linear systems(SLS) with unknown latent space dimension, or order, from its noisy input-output data. In particular, we focus on learning a good lower order approximation of the underlying model allowed by finite data. This is achieved by constructing Hankel-like matrices from data and obtaining suitable approximations via SVD truncation where the threshold for SVD truncation is purely data dependent. By exploiting tools from theory of model reduction for SLS, we find that the system parameter estimates are close to a balanced truncated realization of the underlying system with high probability.