Non-asymptotic Identification of LTI Systems from a Single Trajectory
This addresses the challenge of system identification with limited data for applications in control and signal processing, representing an incremental improvement with specific theoretical bounds.
The paper tackles the problem of learning a linear time-invariant dynamical system from a single input/output trajectory, providing finite-time analysis to determine the data needed to achieve a balanced realization with high probability and desired accuracy.
We consider the problem of learning a realization for a linear time-invariant (LTI) dynamical system from input/output data. Given a single input/output trajectory, we provide finite time analysis for learning the system's Markov parameters, from which a balanced realization is obtained using the classical Ho-Kalman algorithm. By proving a stability result for the Ho-Kalman algorithm and combining it with the sample complexity results for Markov parameters, we show how much data is needed to learn a balanced realization of the system up to a desired accuracy with high probability.