Data-Driven H ∞ Output Tracking Control of Linear Discrete-Time Systems

This paper focuses on the problem of H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> output tracking control for linear discrete-time systems with external disturbances. Two cases in which the disturbance is known and unknown are discussed. The matrix S-lemma is introduced to deal with the unknown disturbance. More importantly, Willems et al. Fundamental Lemma shows that the persistently exciting data can represent the input and output behavior of a linear system. By using the collected I/O data of the original system and reference system, a state feedback controller with a specified H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> performance index is designed, which avoids the dependence on system dynamics knowledge and the potential modeling errors. Based on data-driven control (DDC) technology, the design of the controller is simplified and the designed controller ensures that the output of the closed-loop system tracks the output of the reference signal well. Finally, the simulation results of inverted pendulum system (IPS) verify the effectiveness of the proposed method.