Data-Driven $H_{\infty}$ Control for Unknown Piecewise Affine Systems with Bounded Disturbances

This paper studies the data-driven control problem for piecewise affine (PWA) systems with bounded disturbances, in which both the system model and disturbances are unknown. Due to the unknown disturbances, different PWA systems generate the same input-state-output data, making data-based system identification difficult. In view of this issue, a set containing all systems that could generate the given input-state-output data is constructed in terms of quadratic matrix inequalities (QMIs). The matrix S-lemma is then used to design an
$H_{\infty}$
controller for all these systems. The proposed data-driven
$H_{\infty}$
control method guarantees the internal stability and prescribed performance of the closed-loop system only based on input-state-output data. The effectiveness of the proposed methods is illustrated by a single-link robot arm control system.