Data-Driven Trajectory Tracking Control Design for Unknown Linear Systems via a Nonminimal State-Space Model

This work investigates the zero-error tracking problem for linear systems with unknown dynamics. The proposed method integrates a data-driven system model with an auxiliary system for error characterization. First, a nonminimal state-space (NMSS) model is constructed from historical input-output data. Then, an auxiliary system is formulated by leveraging the common minimal polynomial shared by the disturbance and reference trajectory. The stabilizability and detectability of the auxiliary system are rigorously verified, thereby guaranteeing the existence of a unique positive semidefinite solution to the Riccati equation. Inspired by reinforcement learning (RL) principles, a data-driven output-feedback optimal tracking controller is developed by iteratively learning the optimal Q-function. The theoretical superiority of the proposed controller over existing approaches is established. Simulation results further demonstrate its effectiveness in addressing the tracking problem subject to measurement delays and unmeasurable disturbances.