Hybrid Partial-Data-Driven H∞ Robust Tracking Control for Linear Stochastic Systems with Discrete-Time Observation of Reference Trajectory

Abstract

A hybrid robust $H_{\infty }$ tracking-control design method is studied for linear stochastic systems in which the parameters of the reference system are unknown but inferred from discrete-time observations. First, the reference system parameters are estimated by the least-squares method, and a corresponding data-dependent augmented system is constructed. Second, a Riccati matrix inequality is established for these systems, and a state-feedback $H_{\infty }$ controller is designed to improve tracking performance. Third, to mitigate large tracking errors, an error-feedback control scheme is introduced to compensate for dynamic tracking deviations. These results yield a hybrid control framework that integrates data observation, state-feedback $H_{\infty }$ control, and error-feedback $H_{\infty }$ control to address the tracking problem more effectively. Two numerical examples and one practical example demonstrate the effectiveness of the proposed method.