Optimal Output–Feedback Tracker Design of Linear Quadratic Tracking Problem Using High-Order Filter and Incremental Data Adaptive Dynamic Programming

In this study, a novel optimal tracker is developed for the linear quadratic tracking (LQT) problem using an output–feedback adaptive dynamic programming (ADP) framework. By leveraging the minimal polynomial of the exosystem matrix, we parameterize the steady-state input, state, and output, and incorporate them into the performance index of the LQT formulation. Unlike existing studies on LQT, in this study, we introduce a high-order filter to make the signals related to the high-order derivatives of the system output and input observable. Subsequently, we develop an incremental data ADP algorithm to learn the optimal dynamic output–feedback tracker, eliminate the impact of high-order filtering error and state reconstruction error on the iterative learning equation (ILE) within a specified time. Finally, the comprehensive simulation results show the effectiveness of the proposed output–feedback tracker.