A finite-sample bound for identifying partially observed linear switched systems from a single trajectory
This work addresses system identification for control and signal processing, providing theoretical guarantees for a specific algorithm, but it is incremental as it extends existing methods to a new setting.
The paper tackles the problem of identifying linear switched systems from a single trajectory by deriving a finite-sample probabilistic bound on parameter estimation error, ensuring statistical consistency under quadratic stability assumptions.
We derive a finite-sample probabilistic bound on the parameter estimation error of a system identification algorithm for Linear Switched Systems. The algorithm estimates Markov parameters from a single trajectory and applies a variant of the Ho-Kalman algorithm to recover the system matrices. Our bound guarantees statistical consistency under the assumption that the true system exhibits quadratic stability. The proof leverages the theory of weakly dependent processes. To the best of our knowledge, this is the first finite-sample bound for this algorithm in the single-trajectory setting.